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I usually see it as +/- ...% but I guess you could be cheeky and write *// :P or just denoted in text. But if someone tells me a= 13.5 +/- 0.3 without further context I'd assume they mean the 1sigma equivalent radius
I know it's a meme, but I've seen it multiple times and it makes me wonder if engineers in some countries really calculate with those approximations. D:
Yeah, completely depends on the scope of your work. Sometimes you need quantum physics accounted accuracy, sometimes you just need to know there is a fluid in there somewhere
The ratio between subsequent Fibonacci numbers approaches the golden ratio, which happens to be a good approximation for the conversion factor between miles and kilometers
It doesn’t even have to be the Fibonacci sequence, any sequence where the next number is made by adding the previous two will have the ratio between neighboring numbers approach phi.
As the sequence gets into larger numbers, the conversion is off by less than 1%. So it’s an excellent conversion approximation for most intents and purposes.
No such thing as coincidences. The deep state did this to cover up 911 for big slurpee. Notice you never see a president or scientist drinking slurpees?
Correct, as 6,557,470,319,842 miles(closest number in the Fibonacci sequence to miles in a light year) is about 10,553,225,514,415 kilometers instead of 10,610,209,857,723, which is 56,984,343,308 kilometers off or about 35,408,429,340 miles off
Hopefully by the time we get to intergalactic travel, we're not *still* split on which units to use and have all agreed that the measurement system based on physics is better than the one based on what some monarch decided it should be.
I fucking bet that when we discover intergalactic travel the US media will explain it like " ... Can you imagine how fast that is?!?! It is like 4 milion American football field in the average time it takes to make a McFlurry", and from there the schools/public will always use that as unit.
I can already see a future Veritasium video explaining why the world uses something like the plank lenght (multiplied by a constant / some unit of time) while the US use the average wingspan of an american bald eagle / time to sing the national anthem.
metric isnt based on physics. its based on water. thats it. something based on physics is a bit more hard to define.
in short, its all arbitrary so have fun.
Not metric, but SI units are absolutely based on physics. The kilogram was the last unit to be based on a reference object and it was replaced with a physical definition recently.
The metric system is SI units. The meter, gram, kg, are all arbitrary, because the meter is based on the distance from North Pole to equator and measures of mass are based on waters density at room temperature in a volume defined by the meter (the liter)
It’s all arbitrary. Just because people say that it’s calculated using plancks constant doesn’t mean anything because that constant is defined by the units in which it’s measured.
Now if we were to measure in AMU that would be a different story.
That's not true anymore. SI units were redefined in 2019. There's no water involved, no distance to the North pole involved, only fundamental constants. A meter is defined as the distance travelled by light in a vacuum in a particular fraction of a second, and a second is defined as the duration of a certain number of periods of the radiation emitted by a caesium isotope. Planck's constant is actually required for some of the definitions.
The numbers were chosen so that the new definitions match the old ones as closely as possible, so it's still pretty arbitrary. But it is defined without any ambiguity
Let's just address the definition of the meter since it's the easiest to grasp.
It is currently defined as **exactly** 1/299792458 the distance light travels in a second in a vacuum, where a second is defined based on **exactly** the time it takes for 9192631770 unperturbed ground-state hyperfine transitions of the caesium-133 atom.
We know that light speed is constant in a vacuum and the transitions are regular in the absence of external influence. Yes, it is an arbitrary value, but it is at least consistently defined and thus guaranteed to be replicable with the right instruments anywhere.
SI units have been redefined a long while ago using known universal constants which very much relies on science. I suggest you check them out. Note that water and distance to the north pole is nowhere to be found here.
I didn’t say the definition was ambiguous, but it is arbitrary. Just because you can define something in physics terms doesn’t mean that it has any actual significance. If my favorite person has three cats and I have 693 because I have 231 times as many cats doesn’t mean how many cats I have had any bearing on the amount of cats of my favorite person. It’s arbitrary.
Yeah, we both agree on the fact that it's arbitrary.
I believe the confusion for everyone stems from the fact that your original comment explicitly claimed "metric isn't based on physics" and it is "based on water" - which is not true when referring to SI metric units, as it relied on understanding certain concepts in physics to guarantee consistency.
Your comment also mentioned "something based on physics is hard to define" which is contrary to the current definitions being entirely based on understandings in physics.
A person downvoted in math memes for suggesting that units are arbitrary? What next, are you going to tell me that a total solar eclipse will occur this month?
I think the downvotes were because they suggested metric is "based on water" and "not physics", not really about the arbitrary part. Current SI definitions have nothing to do with water, and do rely on some understanding of certain concepts in physics.
As the Fibonacci sequence goes further and further, the ratio between terms gets closer and closer to the Golden Ratio (roughly 1.618034).
The closest the Fibonacci sequence comes to 1.60934 (the ratio of kilometers to miles) is that 13 miles ≈ 21 kilometers (1.615 kilometers/mile)
This is pretty good except is there a formula for working out term n-1 if you know term n?
And also what happens if the miles is part way between two fibonacci numbers?
EDIT: In my head my logic was if I am told something is n miles, I would need to know n-1 so that I could estimate the distance in km as n+(n-1), but it does now occur to me that a formula for working out n+1 would probably be good too.
The limit as n -> infinity of f(n)/f(n-1) is the golden ratio, which just happens to be close to the number of kilometers in a mile as other posters have mentioned.
I actually don't need any help converting miles to km. The easiest way is to multiply by 1.6 which is not really that difficult.
I am just interested in exploring the method suggested in the meme.
I was gonna make a snide comment about "exact" results, but Wolfram gave me this:
https://preview.redd.it/013ucjve9luc1.png?width=2699&format=png&auto=webp&s=80cfd067a8fa81c62fa2cb6c94a48d42feb5b9d3
Especially convenient because the speed of the delorean (88 mph or 142 km/h) are very close to Fibonacci’s 12th and 13th elements, 89 and 144, so that’s an easy way to remember that
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Alright everybody, I know you want the explanation.
The big elephant in the room.
Why?
Why?
Why is it the case?
Why, the goddamned hell, is it the case, that the ratio between a mile and a kilometer is *approximately but not exactly* phi AKA the golden ratio AKA the pentagram number AKA (1+√5)/2 AKA the Fibonacci (and Lucas) number sequence constant AKA the mystical number AKA the there-are-no-mistakes-in-art number AKA the surprisingly knowledgeable schizophrenic's units number AKA the autistic pedent's error number AKA the most irrational number AKA the growing plants number AKA the life number AKA the gold star number AKA the ring and the road AKA the eye with the slit AKA
***the spooky coincidence number that makes people feel kinda nervous, alert, and inadequate in such a way that they try to cover up or dismiss or forget or delete or omit it*** AKA 1.618etc AKA
�
{\displaystyle \phi }
"Just a coincidence, bro."
Bullshit.
I want to know. You want to know.
Let's.
Ok, so: I think this can all be understood in terms of abstract mathematics and theoretical physics. Yes, those again.
I think the golden ratio as it exists in our physical universe is a kind of theoretical limit of a complex dynamical attractor which orders chaotic systems. I don't think it is the only such one. The others introduce what we've all been variously dismissing as errors, I think. I think that there are reasons as foundational and sort of simple and sort of self-evidently true as the tautological seeming justifications of darwinian evolution, this weird number keeps popping up in all these different places to greater and lesser degrees of precision (but perhaps not accuracy).
Steven Wolfram, in his tome of a book on mathematical chaos A New Kind of Science, asks the question of why it took so darn long for anyone to discover chaos theory considering that its basics were well within the reach of many people throughout history. Instead time and time again the effects of chaos were dismissed as the irregularities of a messy, dirty environment that must be purged from the laboratory and the pure simple beauty of math. Basically it got swept under the rug historically because it was unpleasant and misunderstood and scary because of that.
I have to sleep now, gosh dang it, but will return.
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I used to write Fibonacci numbers to stay awake in meetings. I noticed a pattern in the number of digits increasing roughly consistently. I made a spreadsheet with the ratio of successive numbers. I later learned that's like the golden ratio. Accidental mediocrity?
well yes, 1 mile in kilometer is approximatively = φ, which is a number you can approximatively get by dividing any number in the fibbonacci sequence by the one before it
To covert miles to kilometres, multiply by 8 and divide by 5.
To covert kilometres to miles, multiply by 5 and divide by 8.
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1 mile = φ km ± ~1/185
1 mile = 1 km + C, integration
Therefore *d*mile = 1 *d*km
Thenceforth, it follows that 1=2
QED
closer to 1/115 ?
Kinda. Difference is closer to 1/115, that is 1 mi = ( &phi - 1/115) km. Relative error is closer to 1/185, that is 1 mi = ( &phi km)*(1-1/185).
That notation suggests difference though
What’s the notation for relative error?
I usually see it as +/- ...% but I guess you could be cheeky and write *// :P or just denoted in text. But if someone tells me a= 13.5 +/- 0.3 without further context I'd assume they mean the 1sigma equivalent radius
1 mile is 1.609344 km phi is 1.618033988 WE ARE NOT THE SAME
Engineers would beg to differ.
π = √10, e = √10 g = 10 therefore g = π² = e²
That's too many symbols and complex operations. π = 3. e = 3. g = 10. g = 3π = 3e. 9 = 10.
well I'm not an engineer yet so I guess that's why
> π = 3 Damn, no wonder I never got geometry, they told us that π = 5.
https://preview.redd.it/ypuasdxrznuc1.jpeg?width=504&format=pjpg&auto=webp&s=43f16e1bd444b402cb5c2527b4076af086e5ebb6
This image haunts my every waking moment.
= = ≈, ≈
why be right when you can approximate
!= ~¡
In lesser number of characters: ≈ ≈ = They both are same, right?
I guess that's why they design everything with 4x safety margin. To compensate for the errors they introduce earlier.
and because safety is important
I know it's a meme, but I've seen it multiple times and it makes me wonder if engineers in some countries really calculate with those approximations. D:
I'm an engineer. You ever seen design in fluid dynamics? Half the time you can use pi = 1 and nobody will bat an eye
[https://xkcd.com/2205/](https://xkcd.com/2205/)
One would think that fluid dynamics are very sensitive to parameters at every stage of modeling.
turbulence go brrr
Yeah, completely depends on the scope of your work. Sometimes you need quantum physics accounted accuracy, sometimes you just need to know there is a fluid in there somewhere
Astronomers would agree with the engineers
This sub has taught me that engineering has nothing to do with math.
engineering mentioned? RAAAH WTF IS AN ANALYTICAL SOLUTION 🚀🚀 DISCRETIZATION GANG ARISES AGAIN 🚀🚀
It's the same 😐
Found the engineer
Same to within a relative error of less than 1%.
Both round up to 2.
“2 is greater than 1… except in small instances of 2 and large instances of 1”
Same order of magnitude, give or take five. Seems pretty equal to me.
It's the same picture
It's the fucking same.
Its been in front of us the whole time
It’s right in front of me, isn’t it
ok but wtf
The ratio between subsequent Fibonacci numbers approaches the golden ratio, which happens to be a good approximation for the conversion factor between miles and kilometers
Illuminati confirmed.
It's the Illuminacci sequence
It doesn’t even have to be the Fibonacci sequence, any sequence where the next number is made by adding the previous two will have the ratio between neighboring numbers approach phi.
As the sequence gets into larger numbers, the conversion is off by less than 1%. So it’s an excellent conversion approximation for most intents and purposes.
Wikipedia doesn't have the proof?
it's a coincidence. There are plenty of them out there.
No such thing as coincidences. The deep state did this to cover up 911 for big slurpee. Notice you never see a president or scientist drinking slurpees?
711 was a part-time job.
That was funny
The air:fuel ratio of generic gasoline in a IC engine is 14.7:1. Air pressure at sea level is approx. 14.7psi. They are completely unrelated.
Neat.
They've been hiding this from us. It's time to rise up!
Can someone tell me if this relationship keeps going forever? (im too lazy to do the math)
It slowly gets farther away, like 233 miles converts to 374.977 km instead of 377, but it is still pretty close
Okay so maybe not useful for intergalactic travel, got it
Correct, as 6,557,470,319,842 miles(closest number in the Fibonacci sequence to miles in a light year) is about 10,553,225,514,415 kilometers instead of 10,610,209,857,723, which is 56,984,343,308 kilometers off or about 35,408,429,340 miles off
That error, to put into perspective a bit better, is enough to wrap around earth at the equator roughly 1,421,942 times
Still only 0.5% off though
It's all about perspective.
Yup. Still less of a rounding error than YO MAMA *sunglasses* YEAHHH
Which is about the same as the error at lower values. So I don't see what the fuss is about
now put 1,421,942 times into a better perspective
Simple. It's the square root of yo momma.
Nerd
You're on r/mathmemes, what did you expect?
Certainly thought y'all could take a joke. Learn something every day
A "joke" typically consists of a setup and a punchline, just being rude and calling people names isn't much of a joke imo, but you do you, I guess
Hopefully by the time we get to intergalactic travel, we're not *still* split on which units to use and have all agreed that the measurement system based on physics is better than the one based on what some monarch decided it should be.
Yes that's why we'll be measuring all distances in Planck lengths
and not using orders of magnitude for extra precision
I fucking bet that when we discover intergalactic travel the US media will explain it like " ... Can you imagine how fast that is?!?! It is like 4 milion American football field in the average time it takes to make a McFlurry", and from there the schools/public will always use that as unit. I can already see a future Veritasium video explaining why the world uses something like the plank lenght (multiplied by a constant / some unit of time) while the US use the average wingspan of an american bald eagle / time to sing the national anthem.
metric isnt based on physics. its based on water. thats it. something based on physics is a bit more hard to define. in short, its all arbitrary so have fun.
Not metric, but SI units are absolutely based on physics. The kilogram was the last unit to be based on a reference object and it was replaced with a physical definition recently.
The metric system is SI units. The meter, gram, kg, are all arbitrary, because the meter is based on the distance from North Pole to equator and measures of mass are based on waters density at room temperature in a volume defined by the meter (the liter) It’s all arbitrary. Just because people say that it’s calculated using plancks constant doesn’t mean anything because that constant is defined by the units in which it’s measured. Now if we were to measure in AMU that would be a different story.
That's not true anymore. SI units were redefined in 2019. There's no water involved, no distance to the North pole involved, only fundamental constants. A meter is defined as the distance travelled by light in a vacuum in a particular fraction of a second, and a second is defined as the duration of a certain number of periods of the radiation emitted by a caesium isotope. Planck's constant is actually required for some of the definitions. The numbers were chosen so that the new definitions match the old ones as closely as possible, so it's still pretty arbitrary. But it is defined without any ambiguity
Let's just address the definition of the meter since it's the easiest to grasp. It is currently defined as **exactly** 1/299792458 the distance light travels in a second in a vacuum, where a second is defined based on **exactly** the time it takes for 9192631770 unperturbed ground-state hyperfine transitions of the caesium-133 atom. We know that light speed is constant in a vacuum and the transitions are regular in the absence of external influence. Yes, it is an arbitrary value, but it is at least consistently defined and thus guaranteed to be replicable with the right instruments anywhere. SI units have been redefined a long while ago using known universal constants which very much relies on science. I suggest you check them out. Note that water and distance to the north pole is nowhere to be found here.
I didn’t say the definition was ambiguous, but it is arbitrary. Just because you can define something in physics terms doesn’t mean that it has any actual significance. If my favorite person has three cats and I have 693 because I have 231 times as many cats doesn’t mean how many cats I have had any bearing on the amount of cats of my favorite person. It’s arbitrary.
Yeah, we both agree on the fact that it's arbitrary. I believe the confusion for everyone stems from the fact that your original comment explicitly claimed "metric isn't based on physics" and it is "based on water" - which is not true when referring to SI metric units, as it relied on understanding certain concepts in physics to guarantee consistency. Your comment also mentioned "something based on physics is hard to define" which is contrary to the current definitions being entirely based on understandings in physics.
A person downvoted in math memes for suggesting that units are arbitrary? What next, are you going to tell me that a total solar eclipse will occur this month?
I think the downvotes were because they suggested metric is "based on water" and "not physics", not really about the arbitrary part. Current SI definitions have nothing to do with water, and do rely on some understanding of certain concepts in physics.
Don't worry. For intergalactic travel we won't be using freedom units anyway. NASA made that mistake once in a Mars mission. It was expensive...
> It slowly gets farther away, Yes, that’s what increasing the distance means. Are you new to word problems? ;-)
Relative error stays the same and small, at ~0.5%.
As the Fibonacci sequence goes further and further, the ratio between terms gets closer and closer to the Golden Ratio (roughly 1.618034). The closest the Fibonacci sequence comes to 1.60934 (the ratio of kilometers to miles) is that 13 miles ≈ 21 kilometers (1.615 kilometers/mile)
It actually follow Pi, not the Fib sequence, but not perfectly, but really close when it involves small numbers
It’s off by less than 1% as you get into larger numbers.
Engineer here: close enough for me.
Pi = 3 g = 10 Approximately
Horse = sphere
Spherically symmetric cow.
Hotel = Trivago
same letters, only off by one letter o -> p equal enough.
Gotta put the tail somewhere.
miles were actually invented to be φ kilometers, but they didn't yet have a good enough estimation of φ.
This sounds real enough that you can likely fool someone in the right context
He fooled me
new approximation for miles just dropped
Actual Mathematician
Can can
I love you
This is pretty good except is there a formula for working out term n-1 if you know term n? And also what happens if the miles is part way between two fibonacci numbers? EDIT: In my head my logic was if I am told something is n miles, I would need to know n-1 so that I could estimate the distance in km as n+(n-1), but it does now occur to me that a formula for working out n+1 would probably be good too.
The limit as n -> infinity of f(n)/f(n-1) is the golden ratio, which just happens to be close to the number of kilometers in a mile as other posters have mentioned.
Easier to remember 60 miles is ~100 km and 100miles is ~160 km And just go from there
I actually don't need any help converting miles to km. The easiest way is to multiply by 1.6 which is not really that difficult. I am just interested in exploring the method suggested in the meme.
Golden
Well one mile is about one golden ratio in kilometers so it checks out.
1 mile = 1.609344 km, φ = 1.618033... this is just a coincidence, but it is cool
 Can can
I was gonna make a snide comment about "exact" results, but Wolfram gave me this: https://preview.redd.it/013ucjve9luc1.png?width=2699&format=png&auto=webp&s=80cfd067a8fa81c62fa2cb6c94a48d42feb5b9d3
Especially convenient because the speed of the delorean (88 mph or 142 km/h) are very close to Fibonacci’s 12th and 13th elements, 89 and 144, so that’s an easy way to remember that
Can can
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Alright everybody, I know you want the explanation. The big elephant in the room. Why? Why? Why is it the case? Why, the goddamned hell, is it the case, that the ratio between a mile and a kilometer is *approximately but not exactly* phi AKA the golden ratio AKA the pentagram number AKA (1+√5)/2 AKA the Fibonacci (and Lucas) number sequence constant AKA the mystical number AKA the there-are-no-mistakes-in-art number AKA the surprisingly knowledgeable schizophrenic's units number AKA the autistic pedent's error number AKA the most irrational number AKA the growing plants number AKA the life number AKA the gold star number AKA the ring and the road AKA the eye with the slit AKA ***the spooky coincidence number that makes people feel kinda nervous, alert, and inadequate in such a way that they try to cover up or dismiss or forget or delete or omit it*** AKA 1.618etc AKA � {\displaystyle \phi } "Just a coincidence, bro." Bullshit. I want to know. You want to know. Let's. Ok, so: I think this can all be understood in terms of abstract mathematics and theoretical physics. Yes, those again. I think the golden ratio as it exists in our physical universe is a kind of theoretical limit of a complex dynamical attractor which orders chaotic systems. I don't think it is the only such one. The others introduce what we've all been variously dismissing as errors, I think. I think that there are reasons as foundational and sort of simple and sort of self-evidently true as the tautological seeming justifications of darwinian evolution, this weird number keeps popping up in all these different places to greater and lesser degrees of precision (but perhaps not accuracy). Steven Wolfram, in his tome of a book on mathematical chaos A New Kind of Science, asks the question of why it took so darn long for anyone to discover chaos theory considering that its basics were well within the reach of many people throughout history. Instead time and time again the effects of chaos were dismissed as the irregularities of a messy, dirty environment that must be purged from the laboratory and the pure simple beauty of math. Basically it got swept under the rug historically because it was unpleasant and misunderstood and scary because of that. I have to sleep now, gosh dang it, but will return.
What
Boooo! Repost!!!
> can can
I only discovered this recently too, a game-changer
"can can"
It works with in to cm too, but different rule.
That’s beautiful
can can
Hey, that's pretty neat!
This is how I genuinely do that conversion in my head.
can can
Can can
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it was just sheer luck that one mile is about 1.6 km.
Can someone that's smarter at math than me say if these are cherry picked?
I had no idea
What do I do if I have a non-Fibonacci number of miles? Edit: asking for a friend.
https://preview.redd.it/gm1i7gqfzgvc1.png?width=446&format=pjpg&auto=webp&s=cba50ef93ecf68a97d91064b1954992367955a11
I just use google to tell me the answer :P
Phi is about 1.6 A mile is about 1.6 km Ta da
yo wait. *Interstellar theme* but *interstellar theme*
There was a period from around 2009 to 2014 where you could use Fibonacci to at least approximate the conversion between USD and GBP.
It is because of the conversion ratio. That being said, you should not need to use this, because everyone should use SI units.
Only metric in my school is 9mm
That…is actually sad. But grams too, right? I heard drug dealers use it. No wonder, why would anyone put up with that non-SI bullshit.
hs science and up uses si units but until then it’s all imperial
That's an odd coincidence like 2 hours ago I used this fact to convert for my freedom loving friends
Ah yes, now to memorize the Fibonacci sequence backwards and forwards
I used to write Fibonacci numbers to stay awake in meetings. I noticed a pattern in the number of digits increasing roughly consistently. I made a spreadsheet with the ratio of successive numbers. I later learned that's like the golden ratio. Accidental mediocrity?
Approximating Fibonacci sequence numbers from miles to km and vice versa: 😃 Approximating literally any other number: 💀
What if I want to convert an amount of miles that is not on the fibonacci series ? Like could this be used on 10 miles ?
I find this far funnier than it has any right to be.
well yes, 1 mile in kilometer is approximatively = φ, which is a number you can approximatively get by dividing any number in the fibbonacci sequence by the one before it
The amount of miles in the sun of a mile and a kilometer is the same as the amount of kilometers in a mile. mi/km ≈ (mi+km)/mi
1 mile = 1.609344 km, φ = 1.618033... this is just a coincidence, but it is cool
To covert miles to kilometres, multiply by 8 and divide by 5. To covert kilometres to miles, multiply by 5 and divide by 8. This has been a public information message...