Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

roitman.io

Post reply on HN
Print view View original

161–170 of 352 posts

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

#161

Post by mistercow »

euroderf wrote: post #117
mistercow wrote: post #19

Earlier quoted context omitted.

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 intere…

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

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.

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

#162

Post by gpvos »

fireattack wrote: post #153

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 Sty…

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.

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

#163

Post by phkahler »

usaar333 wrote: post #96
phkahler wrote: post #69

Earlier quoted context omitted.

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.

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

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.

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

#164

Post by lutusp »

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 ...

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

#165

Post by mistercow »

anon457437 wrote: post #159
mistercow wrote: post #149

Earlier quoted context omitted.

Huh, interesting point. Writing unambiguously is ridiculously hard.

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.

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.

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

#166

Post by [deleted] »

john-aj wrote: post #145
klabb3 wrote: post #134

Earlier quoted context omitted.

Another one would be philosophy: there’s nothing, something and everything. Or logic: ∃, ¬∃ and ∀. Just rambling here, but seems like universal concepts across fields.

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 in…

[deleted]

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

#167

Post by 29athrowaway »

lutusp wrote: post #164

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,…

The best is sum(1, 36)

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

#168

Post by Ekaros »

Someone wrote: post #112
lupire wrote: post #88

Earlier quoted context omitted.

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.

> 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…

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.

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

#169

Post by mjburgess »

twojacobtwo wrote: post #151
mjburgess wrote: post #132

Earlier quoted context omitted.

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.

> 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.

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.

Post reply on HN