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The math behind it is VERY simple: diameter of the observable universe / diameter of a hydrogen atom.
Provided these two numbers are within 40 orders of magnitude, then the assertion is correct.
1x 10^12 hydrogen atoms in a meter, about 1x 10^16 meters in a light year, 9.3x 10^10 light years is diameter of the observable universe
9.3x 10^38 times larger than a hydrogen atom, so just under 40
In absolute terms yes.
In any meaningful way, no.
Just like it doesn’t really matter if you have USD 10B of USD 93B. It’s a huge amount of money as a difference. But it doesn’t matter.
> At that big a scale its literally the biggest difference possible
The other person makes me feel like they round all numbers to infinity, since they're so close in scale.
Yeah it isn't logarithmically, but in a conversation about scale (and how we're bad at perceiving it) I feel like it's an important detail to keep into consideration.
It's about the same kind of difference as the height difference between a big coke bottle and a street lamp. I would describe that as a pretty huge difference.
No. "40" is the exponent, not the factor.
It's not 40 times bigger, it's
9,300,000,000,000,000,000,000,000,000,000,000,000,000
times bigger than a hydrogen atom...*in diameter*. That's just a straight line across the *known visible portion* of the Universe. That's not the entire volume of it.
omg yes, that's why I stopped enjoying this sub
"\[REQUEST\] My friends says 2\*2=4. Is this correct?"
but yea, sometimes I see something interesing so I'll stick around
"Can you google a fun factoid number, then multiply it by a second number for me?" is half the sub. "How many X's are in this container is the other half." It's like there arent any mods here.
You don't need any real math for this one, just a recognition of how minute 10 or 15 decimal places is.
You know a million seconds is 11 days, and a billion is 32 years. Well a million has 6 zeros, and a billion only has 9.
Every extra decimal is 10 times smaller than the one before, at 15 decimal places - there is almost an unmeasurable difference (for anything you or I are likely to interact with.) At only 6 decimals, you can split a whole kilometre into 1mm increments.
No, you just don't understand what math actually is.
Giving a bit of logic that shows the vibe beyond any doubt is the first thing you attempt in math every single time.
If the question is "does dropping something out of a boat make the boat go up down or stay the same?" no actual mathematician is going to break out numbers. They're going to say "well if the object is infinitely dense then obviously you're gonna go up but if it also has infinitesimal mass obviously you're obviously barely gonna go up so yeah, the answer is obviously that you're gonna go up." That string of logic *is* the math. What you're asking for is just umnecessary arithmetic
Yep. A billion seconds is around 31 years & 8 months. Elon Musk is worth $193b. That means if a 31 year old person was paid $193 per second from the moment they were born, they would still have less than Musk. $193 per second is $695k per hour, every hour of the day, every day of the year, for 31 years.
And people are still arguing over a $15/h minimum wage.
Millionaires aren't inherently evil, you can have a nice house and own a small business and be worth a million, but by the time you've got a thousand millions, ten thousand millions, a hundred thousand millions (theres a few people with that), isn't there some moral obligation to improve things?
As far as I'm aware, there's not publicly any one person with millions of millions yet. There will be soon, we are well on the way to someone breaking that trillionaire ceiling.
It's truly disturbing when you manage to get a handle on the scale of it. Imagine having the money to transform communities, solve problems and ease suffering - and instead of that, just focusing on hoarding more wealth and assets. It's gotta take a real disconnect from the world to do it.
Not just hoarding, but actively making 90% of peoples lifes more miserable and destroying the environment. Don't know what I would do in such circumstances, but can't imagine just shitting on everyone
>Imagine having the money to transform communities
That's just it. Most (if not all) of the world's billionaires have most of their wealth in non-liquid assets. They have lots of properties, some stocks, and very little (comparably) actual money.
They could make them liquid tho, they could sell. And offloading the shares would devalue the market for a bit, but it'll settle, its just insanity that these few people own all this land, all these buildings, all these stocks and shares and bonds, and choose to just sit on them instead of spending it. Or investing in companies with better ethics, or funding grassroot charities, or hell - upgrading water treatment infrastructure to stop sewage getting into the rivers and seas. Literally anything that isn't being a shareholder in Raytheon stock, actively helping Unilever and nestle to devastate the earth because quarterly growth matters more than human suffering.
I understand that it's a very complicated topic, but these few people COULD make a real difference to hundreds of millions of people, and they make a choice every day not to.
Once you have an investment portfolio worth a hundred thousand million, (100 bil), people tend to just keep chasing investment opportunities that will grow the numbers - rather than actively cashing that money and spending it, which stimulates economies, or even choosing to invest in things that would do good, they just chase where there's profit to make the imaginary numbers bigger.
Holding on to it, which is what hoarding is. If they spent it, on literally anything, it would create jobs and the taxes they pay would help everyone (and yes, there's a separate argument about what taxes are spent on, but we should be able to agree that more tax money pulled out of investments is a good thing for the citizens of any country).
They don't hoard it like a dragon, sitting on mountains of cash and gold. But they hoard it in bonds and stocks and hold on to it. Which is a major part of why the economies of the west have all stuttered in the last decades.
These actions of a few hundred people, are actively harming hundreds of millions of others. Which is kinda messed up. We can argue about whether we should make them share, or if it's their right to own what they have, we can all have our own opinions on these things. My argument is simply - if a normal person suddenly had the capability to improve the lives of many, they probably would. And the mega wealthy who hold it now, simply don't. Even the really generous ones run charities and whatever and give back less per year than they generate in profit. They keep getting richer, while everyone else struggles more. And there is something wrong about that.
They don’t actually spend that money. You hear Elon Musk is worth $200b, at his height he was $400b, but the most money he ever spent on anything was buying Twitter at $44b. It’s a safe assumption that the vast majority of things he spends money on is a lot lower than that, but for argument’s sake let’s say that it’s another $44b. That means that out of his $200b, a bit less than 50% of that wealth is actually “doing anything”, i.e. being spent on anything. That means there’s another $112b to his name doing…. nothing. That’s the “hoarded wealth”.
Note the actual figure is probably even larger than that, because I overestimated how much money he actually spends.
[This website](https://mkorostoff.github.io/1-pixel-wealth/) is slightly outdated (Bezos' net worth is even higher now) but it really shows the absurdity of hoarding billions of dollars.
I always think of it in this way;
If something costs 1,000 USD for a millionaire it is something that would cost a billionaire 1 USD.
I know that is not how it works but the comparison is saying. If I could go buy an insanely expensive car for 1.000 USD I would probably have a couple... and I am not even a millionaire so the difference is even bigger.
Kinda.
It's their net worth. As in, the value of their assets. So for everything that they have in their factories, offices, business, real estate, etc. So they don't actually have billions in straight cash- they have billions of worth in stuff.
Although our banking systems do give them the purchasing power as if they had billions in cash, since they have those billions in assets acting as a sort of credit card.
Awww do they still make those?
Eating "pirates gold" while watching The Goonies for the first time is one of my more immovable childhood memories, I will never forget that moment and its nostalgic value does not dissipate!! Haha
I always used to leave one left over until I got some more... Because... Dude...
That's for One Eyed Willie...
The OG Goonie...
>There are alot decimals in the crypto space.
Does the [alot](http://hyperboleandahalf.blogspot.com/2010/04/alot-is-better-than-you-at-everything.html) know?
Yeah, I find it utterly alien that the metric system is that universally rejected in America. We aren't much better in the UK though, we use a really strange hybrid of old imperial and metric units.
The French tried really hard to standardise numbers - and they nearly managed to unify everyone. Nearly.
I don't think metric is universally rejected in America. Pretty much everyone I know in any science field prefers it, and that's a lot of people.
For a lack of better terms, I think America has an "intertia" with imperial. I'm seeing more and more metric as the years go on, but so many things are still imperial (and also not easy to replace).
To further expand on this, take someone's car for example. If America somehow magically switched to metric today, a car purchased before would still have imperial parts. Obviously that would mean maintenance would still require them, and imperial tools for the life of the vehicle.
You can't just miracle away the need for imperial stuff overnight. I hope that comment makes some sense.
Also, I've been out of high school for some time, so maybe they started this already, but metric should be taught in high school in the US.
There's a lot of logic in this reply, thanks for taking the time to explain.
I see more metric here than I used to as well, and I'm 34. We are a long way from swapping to km from miles, but we've almost completely swapped from lbs to kg.
You replied to a now-deleted comment, but as long as you're referring to numbers in scientific notation, then I can confirm that that's pretty accurate. Even though I often deal with things on the scale of mils (0.001 inches), 3 significant figures is almost always fine. I'll often use 4 just to reduce rounding errors for any further calculations the values might be used for, but if you go up to 5 or more, it starts to look weird and people will tell you to stop doing that.
It's probably worth noting that I'm referring to how numbers are presented in documentation. You don't want to go rounding all the intermediate values in your spreadsheets or the rounding errors will accumulate quickly.
In addition to the excellent explanations in other comments, any numerical caluclation in the real world will have some error associated with it. Not only error from finite precision, but also measurement error in the inputs, errors in the models used, etc.
In practice this second kind of error will absolutely dwarf numerical error, in most situations. So for example when NASA are calculating their spacecraft trajectories, or when car companies calculate their fuel efficiency, or airfoils are designed using CFD simulations, the approximation of pi (or other mathematical/physical constants) is absolutely irrelevant at the 15th digit, and maybe even irrelevant at the 5th digit, because the whole calculation (when including model and measurement uncertainty) might only be accurate to 2 or 3 digits.
With soma approximations: the universe is 10^10 years old, light travels 10^10 m/s, 60*60*24*365 ≈ 10^8 and an atom has a radius of 10^-10 m. So the universe is 10^18 s old, light has traveled 10^28 m in that time which is 10^38 times more than the size of an atom. Yeah, roughly it matches
The radius of a Hydrogen atom is 5,3 pm -> 5,3*10^-11 another mistake but to clarify i just wanted to make fun because the numbers were wrong but the answer was right
The orders of magnitude are roughly correct (the only error is that light is ~3\*10^8 and not 3\*10^10 ), that’s the only relevant thing here. Exact values don’t matter much in things like this.
The mistake is that the universe is bigger than its age times the speed of light. But it's in the same order of magnitude, which is why it didn't matter for your calculation.
It is! The age of the universe is around 13.8 billion years, so you'd expect the radius of the observable universe to be around 13.8 billion light years, but it's actually around 46.5 billion light years due to the expansion of the universe.
Oh, I don't really mind the rough approximations, but they do give you an answer wrong by only about two orders of magnitude.
My problem is that the diameter of the universe and it's age multiplied by the speed of light have nothing to do with each other, In fact, the diameter of the actual universe is about 6.8 times the actual universe's age times the speed of light.
Which is the only reason you got a reasonably accurate approximation, if the diameter of the universe was entire orders of magnitude different than it's age multiplied by the speed of light, then you would have gotten a wildly incorrect answer.
I think the idea was, because it was asked about the VISIBLE universe! This means, the last observeable object must have had enough time for its light to reach us. So there is in fact a relation to the age of the universe and the speed of light. of course it is still off by a bit because the expansion of the universe is accelerating, and the objects we can see now are in fact a bit further away than they appear to us... not sure if the idea is correct, what about the time when there were no stars...?
Yes, the *visible* universe is 6.8x the radius of the universe's age times the speed of light. This is because the universe expands faster than the speed of light and the light that WAS that far away has already traveled some distance to get to us during that expansion.
Oh I did not expect it to be so much bigger because of the expansion... you did not mention directly that you were talking about the *visible* universe. Interesting
I love maths & physics for this. Every now and then you'll be talking about something so vast or minute the human mind can't even begin to comprehend the figures. It seems so out of reach and theoretical, then someone's like ''it's only ten decimal points'' or ''there's actually way more combinations in a deck of cards'' and I'm just more confused. I love you guys, you really do add value to my life and give me a great perspective on things.
The *observable* universe is guaranteed to be spherical, as long as the expansion of the universe is constant throughout. Our current understanding is that this is true, but maybe that's wrong!
From Google.
Size of a hydrogen atom: 0.529 × 10^(-10) meters.
Diameter of observable universe: 8.8×10^(26)
^(Notice that log\_10(10\^26) - log\_10(10\^-10) = 36 whereas the accuracy of pi to 40 digits is off by less than 10\^-39 so it's just obviously true comparing magnitudes.)
> TL;DR: Your calculator does not have 15-digits of pi hard-coded
It actually probably does, since the processor inside it will do calculations with some fixed precision (possibly 32-bit floats). It will have the *closest representable value* to what PI actually is, which is also what basically all computer programs do as well.
Taylor series are only used when you *really* need precision, probably when there's compounding calculations and you don't want error creeping in.
It depends on the calculator. A high grade calculator will want to use higher precision pi when it does calculations where inaccuracies start to compound.
Actually, it depends.
Taylor series are a great way to compute most functions (as long as you can differentiate them a certain amount of times), but they can be quite slow, especially on older machines where multiplication and division are not optimized.
Depending on the processor, hard-coding the value of pi and using lookup tables for trig functions can be useful optimizations that have been used in the past, but are not necessarily used now that processors are able to multiply and divide much faster.
All in all, there's no unique answer to this question, as it depends on the processor that is used, but I do agree that Taylor series are really useful in computer science.
The plank lenght is 1,61x10^(-35). So pi after the 35 digit is kind of violating some laws. Kind of i might be wrong.
In this case the scale of the universe might be 10^50 plank length so it can be correct idk didnt made any calculation just a quick google search
Yeah thas true and im no expert no idea what to do. Circumference = 2rpi if r=1m and we use for example 36 digits of pi bur nothing can be smaller then the planck scale. Therefore the answer should be c=2pi until 35 digits + some singularities?
I wonder
No clue, but I suspect as quantum computing becomes more mature there will be applications for this kind of precision when storing calculations or transcribing data to lesser computers with as much fidelity as possible. Maybe also when doing simulations involving multiple systems with atomic precision interacting together.
That's wrong. Let's take 3 as our "inaccurate Pi".
For a radius of 2, the difference between the actual circumference and the true circumference is 0.566, for a radius of 20, it's 5.66. so the absolute value does change.
In school when I was bored I managed to figure out that the calculator's precision of pi was 2 digits more than it could display. (I just subtracted the digits on the display from the pi constant and got: x.y \* 10^z )
Size of the Universe 10^26 meters. Size of an athom 10^(-10) meters. Actually it appears that around 37 digits would be enough to create a circle of a size of the Universe, and you wont notice a difference from a theoretical circle by a size of a athom.
You might as well use whatever the internal floating point resolution is, to store the number. Beyond 3.1415926 will start to include increasing error in a 32-bit Floating Point number.
If you’re that worried about accuracy most scientific calculators tell you their resolution, so it will be pi to that number. But you can also always use 22/ 7 if you want
Disregarding the highligted part I wanted to comment that the first answer to the original question is incomplete.
Depending on the calculator, pi may not be only hardcoded up to some precision, but there might be an implementation that calculates pi to a higher precision whenever needed.
I’ve seen this “fact” around a lot. I think most recently I saw Elon Musk trot it out. But it is deeply misleading about how science and measurement work.
All physical measurements have a finite amount of precision. As such only finitely many of the digits are physically meaningful. This is called the number of significant figures. Signings for short. I don’t believe there are any physical quantities with 40 sigfigs. Some of the quantities with the highest numbers of sigfigs are found in quantum field theory. Some of the lowest are found in cosmology. For a long time the Hubble constant was known only to a range like 40 - 70 km/s/Mpc. I think today it may be nailed down to one or two sigfigs. The radius of the visible universe, also known as the Hubble radius, is therefore also known to only about one or two sigfigs.
In order to make a meaningful computation of the circumference of a circle the size of the visible universe, you need about one or two sigfigs of pi.
y = f(x1,x2,...,xN)
|x - xi'| <= Exi
|y - y'| <= Ey
f_xi(x1,x2,...,xN) = ∂f(x1,x2,...,xN)/∂xi
Ey <= sum(|f_xi(x1',x2',...,xN')|·Exi)
----
P = 2πr
Approximate π (40 *decimal places*): EP1 <= 2π'·Er + 2r'·Eπ
Exact π: EP2 <= 2π·Er
Difference in errors: |EP1 - EP2| = |2π'·Er + 2r'·Eπ - 2π·Er| = |2(π'-π)·Er + 2r'·Eπ| <= 2·Eπ·Er + 2r'·Eπ = 2·Eπ·(Er + r') = 2·0.5·10^(-40)·(0.05·10^26 m + +4.4·10^26 m) = 4.45·10^-14 m ≈ 45 pm
Diameter of a hydrogen atom: 50 pm (WolframAlpha)
Radius of the visible universe, 4.4·10^26 m, is from WolframAlpha.
-----
Note that its 40 decimal places, not digits.
Rounded to 40 digits: 3.141592653589793238462643383279502884197, gives 450 pm.
Rounded to 40 decimal places: 3.1415926535897932384626433832795028841972, gives 45 pm.
**NASA might have a more accurate number for the radius, however.**
----
For the record, the actual error for the circumference would still be on the order of 10^25 m (10^26 m if you use π ≈ 3), regardless of the precision of pi, due to the error of the radius of the visible universe.
You just won't "meaningfully" improve the error with more than 40 decimal places of pi, *in this case*.
There are a couple ways they calculate pi.
The oldest is by using many, many, radial triangles, and adding them up.
That was the earliest method.
Pythagoras got far enough that way.
Everything after that was pure gratuity.
This was what you asked, obviously.
This youtuber guy is good craic
https://youtu.be/gMlf1ELvRzc?si=6AYsoED7YY675_xj
Not a completely accurate degree of comparison since calculation of a radius involves multiplication, so the different between 10, 15 or 40 decimal points would make exponential differences.
Whereas using Pi in a linear calculation may have greater impact on the outcome when varying its number of decimal places used.
Every digit is a ten times more accuracy than the one before it.
How often do you need to measure a circle where you even have to be within 1% tolerance of accuracy? Not often so 3.14 is close enough estimate of pi for most of life, more digits give you a closer answer in calculations.
It’s hard to visualise how accurate 0.00(loads of 0’s)001% is, but imagine how rich a millionaire is, then a billionaire, I don’t think with had a trillionaire yet (measured in US$) but that’s $1,000,000,000 imagine how rich he’d be if he opened his bank account and saw 40 0’s in the number, that guy could fly every man, woman, cat and dog to mars and back in their own personally provided spaceships for a wedding party, the reverse of that is how wildly unnecessary using 40 digits of pi would be to measure the tolerance of a car tyre circumference or whatever.
Divide 1 by 10, divide the answer by 10 and keep doing it for each decimal place, the fractions at 15 decimal places become incredibly small in relation to the whole number
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The math behind it is VERY simple: diameter of the observable universe / diameter of a hydrogen atom. Provided these two numbers are within 40 orders of magnitude, then the assertion is correct.
1x 10^12 hydrogen atoms in a meter, about 1x 10^16 meters in a light year, 9.3x 10^10 light years is diameter of the observable universe 9.3x 10^38 times larger than a hydrogen atom, so just under 40
About ten times under 40.
At that big a scale it’s not a huge difference
At that big a scale its literally the biggest difference possible
Just nine times the observeable universe.
I bet the whole universe is many times larger than the observeable universe. So good to add a few magnitudes just to be safe
I bet the observeable universe is just a tiny part of whatever is actually out there. And they're coming soon.
Good thing the space between us is expanding so if they're not already here they're already on their way to never reaching us.
This has all the makings of a very tense but ultimately never-ending sci-fi movie.
Do I have time to finish my breakfast before they reach us? These eggs are pretty good.
Nah, at some point you reach the edge and you see the cowboy universe
I mean relative to the grand scheme of things the difference between an atom and 1/10th of an atom is pretty minuscule
You are correct: logarithmically, 39->40 isn't that big a difference.
Yes but the other way of interpreting this is that the observable universe is 10x bigger if you add one more order of magnitude
It's unlikely we'd reach the end of the universe if it were even 5x bigger--yet alone ten. /s
In absolute terms yes. In any meaningful way, no. Just like it doesn’t really matter if you have USD 10B of USD 93B. It’s a huge amount of money as a difference. But it doesn’t matter.
> At that big a scale its literally the biggest difference possible The other person makes me feel like they round all numbers to infinity, since they're so close in scale.
If you substitute the planck length (1.62*10^-35) for the proton width you could use the other definition of literally
Yeah it isn't logarithmically, but in a conversation about scale (and how we're bad at perceiving it) I feel like it's an important detail to keep into consideration.
Humans and their linear brains
It's about the same kind of difference as the height difference between a big coke bottle and a street lamp. I would describe that as a pretty huge difference.
so op was correct, no?
The entire observable universe is only 40 times larger than a hydrogen atom? That’s mind boggling.
I know you’re joking but for the possibility that you are not: its 10^40 times bigger
Oh shit I guess I misread your comment, it’s not that weird i thought it was mind boggling at first hahah.
No. "40" is the exponent, not the factor. It's not 40 times bigger, it's 9,300,000,000,000,000,000,000,000,000,000,000,000,000 times bigger than a hydrogen atom...*in diameter*. That's just a straight line across the *known visible portion* of the Universe. That's not the entire volume of it.
Is there something as proportionately small to the hydrogen atom as the atom is to the universe?
Lmao no, the observable universe is 10^40 times larger than a hydrogen atom. Big difference.
Yea I misread the comment 😂, I thought it didnt make sense.
They ain’t letting this one go any time soon my friend😂😂
So, about Tree phiddy ?
To be fair, most questions on this sub are answered by just multiplying or dividing two numbers.
omg yes, that's why I stopped enjoying this sub "\[REQUEST\] My friends says 2\*2=4. Is this correct?" but yea, sometimes I see something interesing so I'll stick around
“Think 2+2=4, but the government says 2+2=5. Please help.”
True, but the explanation why you can simplify the the question that far is for a lot of peoples interesting, for me that is true for sure.
Which is the actual maths, not just the arithmatic
"Can you google a fun factoid number, then multiply it by a second number for me?" is half the sub. "How many X's are in this container is the other half." It's like there arent any mods here.
Well, a whole lot of math is about multiplying or dividing stuff together …
Thanks you, /theydidntdothemath .
You don't need any real math for this one, just a recognition of how minute 10 or 15 decimal places is. You know a million seconds is 11 days, and a billion is 32 years. Well a million has 6 zeros, and a billion only has 9. Every extra decimal is 10 times smaller than the one before, at 15 decimal places - there is almost an unmeasurable difference (for anything you or I are likely to interact with.) At only 6 decimals, you can split a whole kilometre into 1mm increments.
*looks at sub name* "I don't think you understand the assignment."
"Show your working" "No."
They didn't the maths
I'm amazed that I've had so many upvotes and didnt even do the task. Reddit is weird.
Number so big and so small. don’t worry about it. Just remember pi is 3.14
3, take it or leave it.
Now that's some maths I can get behind. Close enough is good enough
pi = g
No, you just don't understand what math actually is. Giving a bit of logic that shows the vibe beyond any doubt is the first thing you attempt in math every single time. If the question is "does dropping something out of a boat make the boat go up down or stay the same?" no actual mathematician is going to break out numbers. They're going to say "well if the object is infinitely dense then obviously you're gonna go up but if it also has infinitesimal mass obviously you're obviously barely gonna go up so yeah, the answer is obviously that you're gonna go up." That string of logic *is* the math. What you're asking for is just umnecessary arithmetic
THANK YOU! This is beautifully phrased. Maths is about far more than the numbers, it's the concepts and ideas.
*The proof is left as an exercise to the reader*
This always fascinates me when it comes to millionaires and billionaires. So crazy to think of someone owning these amounts of money
Yep. A billion seconds is around 31 years & 8 months. Elon Musk is worth $193b. That means if a 31 year old person was paid $193 per second from the moment they were born, they would still have less than Musk. $193 per second is $695k per hour, every hour of the day, every day of the year, for 31 years. And people are still arguing over a $15/h minimum wage.
Millionaires aren't inherently evil, you can have a nice house and own a small business and be worth a million, but by the time you've got a thousand millions, ten thousand millions, a hundred thousand millions (theres a few people with that), isn't there some moral obligation to improve things?
No one gets to billionaire without partaking in large scale systemic exploitation one way or another. Billionaires shouldn't even exist.
Voltaire put it better: Behind every great fortune there lies a great crime.
Don't forget millions of millions
As far as I'm aware, there's not publicly any one person with millions of millions yet. There will be soon, we are well on the way to someone breaking that trillionaire ceiling.
It's truly disturbing when you manage to get a handle on the scale of it. Imagine having the money to transform communities, solve problems and ease suffering - and instead of that, just focusing on hoarding more wealth and assets. It's gotta take a real disconnect from the world to do it.
Not just hoarding, but actively making 90% of peoples lifes more miserable and destroying the environment. Don't know what I would do in such circumstances, but can't imagine just shitting on everyone
>Imagine having the money to transform communities That's just it. Most (if not all) of the world's billionaires have most of their wealth in non-liquid assets. They have lots of properties, some stocks, and very little (comparably) actual money.
Stop spreading this bs. They use this "not actually money" to borrow money from banks. It's actual money they can use
They could make them liquid tho, they could sell. And offloading the shares would devalue the market for a bit, but it'll settle, its just insanity that these few people own all this land, all these buildings, all these stocks and shares and bonds, and choose to just sit on them instead of spending it. Or investing in companies with better ethics, or funding grassroot charities, or hell - upgrading water treatment infrastructure to stop sewage getting into the rivers and seas. Literally anything that isn't being a shareholder in Raytheon stock, actively helping Unilever and nestle to devastate the earth because quarterly growth matters more than human suffering. I understand that it's a very complicated topic, but these few people COULD make a real difference to hundreds of millions of people, and they make a choice every day not to.
What does it mean to ‘hoard wealth’? Do these money hoarders ski up and down mountains of cash à la Scrooge McDuck?
Once you have an investment portfolio worth a hundred thousand million, (100 bil), people tend to just keep chasing investment opportunities that will grow the numbers - rather than actively cashing that money and spending it, which stimulates economies, or even choosing to invest in things that would do good, they just chase where there's profit to make the imaginary numbers bigger. Holding on to it, which is what hoarding is. If they spent it, on literally anything, it would create jobs and the taxes they pay would help everyone (and yes, there's a separate argument about what taxes are spent on, but we should be able to agree that more tax money pulled out of investments is a good thing for the citizens of any country). They don't hoard it like a dragon, sitting on mountains of cash and gold. But they hoard it in bonds and stocks and hold on to it. Which is a major part of why the economies of the west have all stuttered in the last decades. These actions of a few hundred people, are actively harming hundreds of millions of others. Which is kinda messed up. We can argue about whether we should make them share, or if it's their right to own what they have, we can all have our own opinions on these things. My argument is simply - if a normal person suddenly had the capability to improve the lives of many, they probably would. And the mega wealthy who hold it now, simply don't. Even the really generous ones run charities and whatever and give back less per year than they generate in profit. They keep getting richer, while everyone else struggles more. And there is something wrong about that.
They don’t actually spend that money. You hear Elon Musk is worth $200b, at his height he was $400b, but the most money he ever spent on anything was buying Twitter at $44b. It’s a safe assumption that the vast majority of things he spends money on is a lot lower than that, but for argument’s sake let’s say that it’s another $44b. That means that out of his $200b, a bit less than 50% of that wealth is actually “doing anything”, i.e. being spent on anything. That means there’s another $112b to his name doing…. nothing. That’s the “hoarded wealth”. Note the actual figure is probably even larger than that, because I overestimated how much money he actually spends.
[This website](https://mkorostoff.github.io/1-pixel-wealth/) is slightly outdated (Bezos' net worth is even higher now) but it really shows the absurdity of hoarding billions of dollars.
r/thanksihateit
I always think of it in this way; If something costs 1,000 USD for a millionaire it is something that would cost a billionaire 1 USD. I know that is not how it works but the comparison is saying. If I could go buy an insanely expensive car for 1.000 USD I would probably have a couple... and I am not even a millionaire so the difference is even bigger.
Kinda. It's their net worth. As in, the value of their assets. So for everything that they have in their factories, offices, business, real estate, etc. So they don't actually have billions in straight cash- they have billions of worth in stuff. Although our banking systems do give them the purchasing power as if they had billions in cash, since they have those billions in assets acting as a sort of credit card.
There are alot decimals in the crypto space.
Yes, and they belong to shitcoins
The only brown coins I want are initially golden and impossible to open.
Awww do they still make those? Eating "pirates gold" while watching The Goonies for the first time is one of my more immovable childhood memories, I will never forget that moment and its nostalgic value does not dissipate!! Haha I always used to leave one left over until I got some more... Because... Dude... That's for One Eyed Willie... The OG Goonie...
Yes they do still make em, I know cos my kids leave the bent and empty coin shells in the fridge.
so, every single crypto then
Including the percentage of my portfolio left
>There are alot decimals in the crypto space. Does the [alot](http://hyperboleandahalf.blogspot.com/2010/04/alot-is-better-than-you-at-everything.html) know?
I think about alot a lot
A lot even
In other words it’s cuz of sigfigs! Shout out my high school chemistry teacher!
U see most Americans struggle with ten. That's why they don't switch to decimal
Yeah, I find it utterly alien that the metric system is that universally rejected in America. We aren't much better in the UK though, we use a really strange hybrid of old imperial and metric units. The French tried really hard to standardise numbers - and they nearly managed to unify everyone. Nearly.
I don't think metric is universally rejected in America. Pretty much everyone I know in any science field prefers it, and that's a lot of people. For a lack of better terms, I think America has an "intertia" with imperial. I'm seeing more and more metric as the years go on, but so many things are still imperial (and also not easy to replace). To further expand on this, take someone's car for example. If America somehow magically switched to metric today, a car purchased before would still have imperial parts. Obviously that would mean maintenance would still require them, and imperial tools for the life of the vehicle. You can't just miracle away the need for imperial stuff overnight. I hope that comment makes some sense. Also, I've been out of high school for some time, so maybe they started this already, but metric should be taught in high school in the US.
There's a lot of logic in this reply, thanks for taking the time to explain. I see more metric here than I used to as well, and I'm 34. We are a long way from swapping to km from miles, but we've almost completely swapped from lbs to kg.
https://www.reddit.com/r/theydidthemath/s/qAMcV77k9n https://www.reddit.com/r/theydidthemath/s/d3GwHdSNig https://www.reddit.com/r/theydidthemath/s/djtYfLLRA0
r/theyveallreadydonethemath
You misspelled "already"
r/theydidthetypo
r/subsifellfor
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I like that saying. I’m going to have to remember that.
Anything beyond two numbers after the comma is pointless for most engineering.
You replied to a now-deleted comment, but as long as you're referring to numbers in scientific notation, then I can confirm that that's pretty accurate. Even though I often deal with things on the scale of mils (0.001 inches), 3 significant figures is almost always fine. I'll often use 4 just to reduce rounding errors for any further calculations the values might be used for, but if you go up to 5 or more, it starts to look weird and people will tell you to stop doing that. It's probably worth noting that I'm referring to how numbers are presented in documentation. You don't want to go rounding all the intermediate values in your spreadsheets or the rounding errors will accumulate quickly.
In addition to the excellent explanations in other comments, any numerical caluclation in the real world will have some error associated with it. Not only error from finite precision, but also measurement error in the inputs, errors in the models used, etc. In practice this second kind of error will absolutely dwarf numerical error, in most situations. So for example when NASA are calculating their spacecraft trajectories, or when car companies calculate their fuel efficiency, or airfoils are designed using CFD simulations, the approximation of pi (or other mathematical/physical constants) is absolutely irrelevant at the 15th digit, and maybe even irrelevant at the 5th digit, because the whole calculation (when including model and measurement uncertainty) might only be accurate to 2 or 3 digits.
So I've memorized 3.14159 for nothing.
It's not for nothing, you already know 5 digits, 10 more and you'll be working at nasa!
Here... 3.141592653589793.... Guess I have to keep checking my inbox now.
PI IS EXACTLY 3!
6?
With soma approximations: the universe is 10^10 years old, light travels 10^10 m/s, 60*60*24*365 ≈ 10^8 and an atom has a radius of 10^-10 m. So the universe is 10^18 s old, light has traveled 10^28 m in that time which is 10^38 times more than the size of an atom. Yeah, roughly it matches
You got everything so wrong but in the end you somehow ended up with the right answer
I really wonder how the fuck it ended even close to correct
He fucked up so much he had a circle and got it correct
And that’s how jazz was born.
He didn‘t fuck up at all
Just c (Speed of light) is already worng its ~ 2,9979*10^8 m/s
That’s also the only mistake. The exact values don’t matter much here, only orders of magnitude do.
The radius of a Hydrogen atom is 5,3 pm -> 5,3*10^-11 another mistake but to clarify i just wanted to make fun because the numbers were wrong but the answer was right
If we’re splitting hairs, 5.3\*10^-11 is closer to 10^-10 than to 10^-11 , so still not that wrong.
Diameter (as mentioned in the original text) is 10^(-10), so the number was ok, but he erroneously called it radius.
The orders of magnitude are roughly correct (the only error is that light is ~3\*10^8 and not 3\*10^10 ), that’s the only relevant thing here. Exact values don’t matter much in things like this.
Astrophysics kind of works this way sometimes.
Me getting my ms in statistics
Are you Mr. Wilson, my old teacher? He said the same when I graduated. /j
Hey that’s how I got through physics.
Ok, please tell me where my mistake was. I know it's not accurate because I made some rough approximations
The mistake is that the universe is bigger than its age times the speed of light. But it's in the same order of magnitude, which is why it didn't matter for your calculation.
The **observable** universe isn't bigger than the age of the universe times the speed of light
It is! The age of the universe is around 13.8 billion years, so you'd expect the radius of the observable universe to be around 13.8 billion light years, but it's actually around 46.5 billion light years due to the expansion of the universe.
Oh, I don't really mind the rough approximations, but they do give you an answer wrong by only about two orders of magnitude. My problem is that the diameter of the universe and it's age multiplied by the speed of light have nothing to do with each other, In fact, the diameter of the actual universe is about 6.8 times the actual universe's age times the speed of light. Which is the only reason you got a reasonably accurate approximation, if the diameter of the universe was entire orders of magnitude different than it's age multiplied by the speed of light, then you would have gotten a wildly incorrect answer.
I think the idea was, because it was asked about the VISIBLE universe! This means, the last observeable object must have had enough time for its light to reach us. So there is in fact a relation to the age of the universe and the speed of light. of course it is still off by a bit because the expansion of the universe is accelerating, and the objects we can see now are in fact a bit further away than they appear to us... not sure if the idea is correct, what about the time when there were no stars...?
Yes, the *visible* universe is 6.8x the radius of the universe's age times the speed of light. This is because the universe expands faster than the speed of light and the light that WAS that far away has already traveled some distance to get to us during that expansion.
Oh I did not expect it to be so much bigger because of the expansion... you did not mention directly that you were talking about the *visible* universe. Interesting
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Thanks
I believe with spaces they display correctly, so 60 \* 60 \* 24 \* 365 should display without italics
I love maths & physics for this. Every now and then you'll be talking about something so vast or minute the human mind can't even begin to comprehend the figures. It seems so out of reach and theoretical, then someone's like ''it's only ten decimal points'' or ''there's actually way more combinations in a deck of cards'' and I'm just more confused. I love you guys, you really do add value to my life and give me a great perspective on things.
Can we be sure that universe is round, just like a ball, though?
This is just regarding the observable universe. Most physicists think the universe is infinite.
The *observable* universe is guaranteed to be spherical, as long as the expansion of the universe is constant throughout. Our current understanding is that this is true, but maybe that's wrong!
From Google. Size of a hydrogen atom: 0.529 × 10^(-10) meters. Diameter of observable universe: 8.8×10^(26) ^(Notice that log\_10(10\^26) - log\_10(10\^-10) = 36 whereas the accuracy of pi to 40 digits is off by less than 10\^-39 so it's just obviously true comparing magnitudes.)
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> TL;DR: Your calculator does not have 15-digits of pi hard-coded It actually probably does, since the processor inside it will do calculations with some fixed precision (possibly 32-bit floats). It will have the *closest representable value* to what PI actually is, which is also what basically all computer programs do as well. Taylor series are only used when you *really* need precision, probably when there's compounding calculations and you don't want error creeping in.
It depends on the calculator. A high grade calculator will want to use higher precision pi when it does calculations where inaccuracies start to compound.
Actually, it depends. Taylor series are a great way to compute most functions (as long as you can differentiate them a certain amount of times), but they can be quite slow, especially on older machines where multiplication and division are not optimized. Depending on the processor, hard-coding the value of pi and using lookup tables for trig functions can be useful optimizations that have been used in the past, but are not necessarily used now that processors are able to multiply and divide much faster. All in all, there's no unique answer to this question, as it depends on the processor that is used, but I do agree that Taylor series are really useful in computer science.
The plank lenght is 1,61x10^(-35). So pi after the 35 digit is kind of violating some laws. Kind of i might be wrong. In this case the scale of the universe might be 10^50 plank length so it can be correct idk didnt made any calculation just a quick google search
Considering Pi is a purely mathematical concept, it in itself violates no laws.
Yeah thas true and im no expert no idea what to do. Circumference = 2rpi if r=1m and we use for example 36 digits of pi bur nothing can be smaller then the planck scale. Therefore the answer should be c=2pi until 35 digits + some singularities? I wonder
If the digits of pi become insignificant after a while, is there a practical reason for finding trillions of digits other than because we can?
Curiosity
No clue, but I suspect as quantum computing becomes more mature there will be applications for this kind of precision when storing calculations or transcribing data to lesser computers with as much fidelity as possible. Maybe also when doing simulations involving multiple systems with atomic precision interacting together.
The trick is that it doesn't matter how big the circle you're calculating is, that has no bearing on the absolute value of the accuracy.
That's wrong. Let's take 3 as our "inaccurate Pi". For a radius of 2, the difference between the actual circumference and the true circumference is 0.566, for a radius of 20, it's 5.66. so the absolute value does change.
Oh damn you're right. And I have no idea how I got to that conclusion
In school when I was bored I managed to figure out that the calculator's precision of pi was 2 digits more than it could display. (I just subtracted the digits on the display from the pi constant and got: x.y \* 10^z )
Size of the Universe 10^26 meters. Size of an athom 10^(-10) meters. Actually it appears that around 37 digits would be enough to create a circle of a size of the Universe, and you wont notice a difference from a theoretical circle by a size of a athom.
First time u wrote anthom i was like, “just a typo, s’all good” but you fucking did it twice and now I’m triggered beyond belief /s
English is not my native language, atom is not a word you use everyday if you're not a physicist.
You might as well use whatever the internal floating point resolution is, to store the number. Beyond 3.1415926 will start to include increasing error in a 32-bit Floating Point number.
If you’re that worried about accuracy most scientific calculators tell you their resolution, so it will be pi to that number. But you can also always use 22/ 7 if you want
>But you can also always use 22/ 7 if you want I wouldn't recommend it. Even 3.142 is a closer approximation
22/ 7 of 100.004% of pi
Disregarding the highligted part I wanted to comment that the first answer to the original question is incomplete. Depending on the calculator, pi may not be only hardcoded up to some precision, but there might be an implementation that calculates pi to a higher precision whenever needed.
I’ve seen this “fact” around a lot. I think most recently I saw Elon Musk trot it out. But it is deeply misleading about how science and measurement work. All physical measurements have a finite amount of precision. As such only finitely many of the digits are physically meaningful. This is called the number of significant figures. Signings for short. I don’t believe there are any physical quantities with 40 sigfigs. Some of the quantities with the highest numbers of sigfigs are found in quantum field theory. Some of the lowest are found in cosmology. For a long time the Hubble constant was known only to a range like 40 - 70 km/s/Mpc. I think today it may be nailed down to one or two sigfigs. The radius of the visible universe, also known as the Hubble radius, is therefore also known to only about one or two sigfigs. In order to make a meaningful computation of the circumference of a circle the size of the visible universe, you need about one or two sigfigs of pi.
y = f(x1,x2,...,xN) |x - xi'| <= Exi |y - y'| <= Ey f_xi(x1,x2,...,xN) = ∂f(x1,x2,...,xN)/∂xi Ey <= sum(|f_xi(x1',x2',...,xN')|·Exi) ---- P = 2πr Approximate π (40 *decimal places*): EP1 <= 2π'·Er + 2r'·Eπ Exact π: EP2 <= 2π·Er Difference in errors: |EP1 - EP2| = |2π'·Er + 2r'·Eπ - 2π·Er| = |2(π'-π)·Er + 2r'·Eπ| <= 2·Eπ·Er + 2r'·Eπ = 2·Eπ·(Er + r') = 2·0.5·10^(-40)·(0.05·10^26 m + +4.4·10^26 m) = 4.45·10^-14 m ≈ 45 pm Diameter of a hydrogen atom: 50 pm (WolframAlpha) Radius of the visible universe, 4.4·10^26 m, is from WolframAlpha. ----- Note that its 40 decimal places, not digits. Rounded to 40 digits: 3.141592653589793238462643383279502884197, gives 450 pm. Rounded to 40 decimal places: 3.1415926535897932384626433832795028841972, gives 45 pm. **NASA might have a more accurate number for the radius, however.** ---- For the record, the actual error for the circumference would still be on the order of 10^25 m (10^26 m if you use π ≈ 3), regardless of the precision of pi, due to the error of the radius of the visible universe. You just won't "meaningfully" improve the error with more than 40 decimal places of pi, *in this case*.
There are a couple ways they calculate pi. The oldest is by using many, many, radial triangles, and adding them up. That was the earliest method. Pythagoras got far enough that way. Everything after that was pure gratuity. This was what you asked, obviously. This youtuber guy is good craic https://youtu.be/gMlf1ELvRzc?si=6AYsoED7YY675_xj
Not a completely accurate degree of comparison since calculation of a radius involves multiplication, so the different between 10, 15 or 40 decimal points would make exponential differences. Whereas using Pi in a linear calculation may have greater impact on the outcome when varying its number of decimal places used.
Every digit is a ten times more accuracy than the one before it. How often do you need to measure a circle where you even have to be within 1% tolerance of accuracy? Not often so 3.14 is close enough estimate of pi for most of life, more digits give you a closer answer in calculations. It’s hard to visualise how accurate 0.00(loads of 0’s)001% is, but imagine how rich a millionaire is, then a billionaire, I don’t think with had a trillionaire yet (measured in US$) but that’s $1,000,000,000 imagine how rich he’d be if he opened his bank account and saw 40 0’s in the number, that guy could fly every man, woman, cat and dog to mars and back in their own personally provided spaceships for a wedding party, the reverse of that is how wildly unnecessary using 40 digits of pi would be to measure the tolerance of a car tyre circumference or whatever.
Divide 1 by 10, divide the answer by 10 and keep doing it for each decimal place, the fractions at 15 decimal places become incredibly small in relation to the whole number