Todays Pi day comes with much remorse. With the passing of Stephen Hawking, it is a big loss to science and scholars worldwide.
I think Neil deGrasse Tyson said it best when he wrote, "His passing has left an intellectual vacuum in his wake. But it's not empty. Think of it as a kind of vacuum energy permeating the fabric of spacetime that defies measure".
Interesting factoid about pi: it's believed to be a "normal number," but no one has been able to prove or disprove it.
A normal number is one whose m-ary expansion contains every n-length sequence of digits with equal probability, where m is any number base. IOW, if pi were normal, and you encoded its expansion in base 128 with ASCII characters, it would contain the text of every book ever written (or not written)! For every statement of fact, its contradiction could also be found somewhere in that expansion.
The Argentinian author Jorge Luis Borges wrote a short story on this theme, "The Library of Babel," which is included in his anthology, Labyrinths. The library is of indefinite size, and its books contain every possible sequence of 25 lexical symbols. Borges riffs on this theme in exquisite detail, making it a very fun read.
Hmm, "The Library of Babel"? I have to check that out.
Sounds like the World Wide Web. Enormously huge and you know there is useful information in there somewhere. But it's really hard to find and mostly surrounded by gibberish.
It's fun to think about these infinite things from time to time. If PI is "normal" then it must contain itself somewhere. An infinite number of times!
Sounds like the World Wide Web. Enormously huge and you know there is useful information in there somewhere. But it's really hard to find and mostly surrounded by gibberish.
........
Boy, you hit that nail on the head. Been searching for information to start on my summer project and so far it seems like the ratio of useful information to gibberish is measured in PPM or in some cases PPB. I'm hoping it's because I am not very good at searching yet and that the ratio will improve as I learn. I have my doubts though.
which rather shows the clout RaspPi now has, with chip vendors beating a path to their door. This press release also hints at the complex supply handling such SBC's venture into.
This bit sounds as little half-baked ?
"The upgraded Pi also now supports power-over-ethernet (PoE), meaning you’ll soon be able to power the device through its ethernet port, though you’ll need to wait for a separate Poe HAT to launch “shortly.”"
They also seem to have bumped into a wall, on the MicroUSB connector, google says that's MAX 1.8A, but a video suggested a 2.5A power supply in needed.
You hadda ask: 3.1415926535897932384626433832795028841
When I was 16, someone bet me $5 that I couldn't memorize pi to 100 digits in five minutes; I won the bet with 150 places, and still remember anywhere from 23 to 45 (37 today). Curiously, I don't get them wrong; when I'm not sure, I know when to stop and never guess wrong. Yeah, this is a weird and probably not very useful skill that has curiously never made it to my resume and that I've probably lost in the ensuing 35 years. But it's fun.
By the way, if the observable universe has a radius of 45 billion light-years, which is about 4.3 x 10^28 cm, so the circumference is about 2.7 x 10^29 cm, you need about 29 digits of pi to get it to within 1 cm. You only gave 11 digits, which is only an accuracy of about 10 trillion km, about 1 light-year. I think my numbers are within an order of magnitude, base pi :-)
EDIT: I didn't see Heater's post, which made me go back and check mine; I forgot to convert from seconds to years. Heater, I think yours is off by a factor of pi, which is a whole lot better than my first attempt, which was off by a factor of 31.6 (2nd EDIT: 100) million.
2nd EDIT: Sorry Heater, you're right; the radius of the observable universe is not simply the age multiplied by the speed of light.
Oh great. With pi = 6.2831854..., the area of a circle would be pi*r^2 / 2. History has prevailed -- thankfully.
-Phil
Addendum: When, oh when!, are we going to get sup and sub reinstated as BBcodes? It's been more than three years, Parallax! We really need these, along with noparse. There are old posts that are still broken without these!
Perhaps I'm too stupid to understand but to my simple mind:
1) Why does a change of base make any difference to the argument? It's just different notation for the same thing.
2) What is the difference between "finite sequences -- of any length" and an infinite sequence? Surely "any" allows the infinite also?
OK, we may have to account for Cantor's countably infinite and other bigger infinities. But hey, we are talking about a transcendental number here which is suspected to be "normal". How big can a thing be?
But, all this must be speculation. As you said it is not proven that PI is a "normal" number. So surely we don't know.
From the Verge article: "The thing is, we don’t actually use diameter to describe circles."
The thing is, we _do_ use diameter to describe circles. Probably 100:1. Drill bits, hockey pucks, celestial bodies, bullet calibers, rocket fairings, welding rods, cake pans, pie plates (can't forget that!), you name it; if it's round, it's nearly always specified in terms of diameter.
BTW, K2's newest Pi appeared on the doorstep on Pi Day. Today it got Stretched. It's simply mind-blowing what happens when you mix those two. It's the Kinepak of the computer world.
Why does a change of base make any difference to the argument?
In the special case of pi and tau, their binary expansions are just a bit shift way from each other. So the entire expansion of each is contained in the other.
What is the difference between "finite sequences -- of any length" and an infinite sequence? Surely "any" allows the infinite also?
Not quite. In a normal number, any finite sequence can be found with equal probability to any other sequence of the same length. So the probability of finding any random infinite sequence is zero. If the infinite decimal expansion of tau existed in the infinite decimal expansion of pi, so would 111111111... . But then pi would rational. But it's not.
DaveJenson
Posts: 375
Comments
A new update to the Raspberry Pi was launched: https://www.raspberrypi.org/forums/viewtopic.php?f=63&t=207863
I can't for the life of me see how one gets PI out of 14/03/2008. Which I reckon is about 0.0023125206475057814
Or 14/03 which I make 4.6 recurring.
I find this numerology faintly annoying.
I think Neil deGrasse Tyson said it best when he wrote, "His passing has left an intellectual vacuum in his wake. But it's not empty. Think of it as a kind of vacuum energy permeating the fabric of spacetime that defies measure".
A normal number is one whose m-ary expansion contains every n-length sequence of digits with equal probability, where m is any number base. IOW, if pi were normal, and you encoded its expansion in base 128 with ASCII characters, it would contain the text of every book ever written (or not written)! For every statement of fact, its contradiction could also be found somewhere in that expansion.
The Argentinian author Jorge Luis Borges wrote a short story on this theme, "The Library of Babel," which is included in his anthology, Labyrinths. The library is of indefinite size, and its books contain every possible sequence of 25 lexical symbols. Borges riffs on this theme in exquisite detail, making it a very fun read.
-Phil
Sounds like the World Wide Web. Enormously huge and you know there is useful information in there somewhere. But it's really hard to find and mostly surrounded by gibberish.
It's fun to think about these infinite things from time to time. If PI is "normal" then it must contain itself somewhere. An infinite number of times!
Not to mention every other number.
Boy, you hit that nail on the head. Been searching for information to start on my summer project and so far it seems like the ratio of useful information to gibberish is measured in PPM or in some cases PPB. I'm hoping it's because I am not very good at searching yet and that the ratio will improve as I learn. I have my doubts though.
Yes, Raspberry Pi 3 Model B+ - interesting.
I also see this press release
https://www10.edacafe.com/nbc/articles/1/1572379/MaxLinears-MxL7704-Power-Management-IC-Powers-Raspberry-Pi-3-Model-B+
which rather shows the clout RaspPi now has, with chip vendors beating a path to their door. This press release also hints at the complex supply handling such SBC's venture into.
This bit sounds as little half-baked ?
"The upgraded Pi also now supports power-over-ethernet (PoE), meaning you’ll soon be able to power the device through its ethernet port, though you’ll need to wait for a separate Poe HAT to launch “shortly.”"
They also seem to have bumped into a wall, on the MicroUSB connector, google says that's MAX 1.8A, but a video suggested a 2.5A power supply in needed.
Eat your heart out, Tau lovers!
In 2009, the United States House of Representatives supported the designation of Pi Day. Wikipedia
That is about as significant as the proposed "Indiana Pi Bill" to define PI as 3.2 in 1897:
https://en.wikipedia.org/wiki/Indiana_Pi_Bill
Hmm.. actually, such ignorance in the powers that be is very significant. And worrying.
3.14159265359
That's good enough to calculate the circumference of the observable universe to a centimeter or so, so it'll do.
-Phil
I think, possibly, maybe, my idea there is that the digits do not matter. The idea of what PI is about does.
Anyway, you will need some more digits there to get to the radius of the known universe: 4.40E28 centimeters.
When I was 16, someone bet me $5 that I couldn't memorize pi to 100 digits in five minutes; I won the bet with 150 places, and still remember anywhere from 23 to 45 (37 today). Curiously, I don't get them wrong; when I'm not sure, I know when to stop and never guess wrong. Yeah, this is a weird and probably not very useful skill that has curiously never made it to my resume and that I've probably lost in the ensuing 35 years. But it's fun.
By the way, if the observable universe has a radius of 45 billion light-years, which is about 4.3 x 10^28 cm, so the circumference is about 2.7 x 10^29 cm, you need about 29 digits of pi to get it to within 1 cm. You only gave 11 digits, which is only an accuracy of about 10 trillion km, about 1 light-year. I think my numbers are within an order of magnitude, base pi :-)
EDIT: I didn't see Heater's post, which made me go back and check mine; I forgot to convert from seconds to years. Heater, I think yours is off by a factor of pi, which is a whole lot better than my first attempt, which was off by a factor of 31.6 (2nd EDIT: 100) million.
2nd EDIT: Sorry Heater, you're right; the radius of the observable universe is not simply the age multiplied by the speed of light.
I still need to remove the excess material "raft", which removes easily...
What you do with it perhaps does:
-Phil
Addendum: When, oh when!, are we going to get sup and sub reinstated as BBcodes? It's been more than three years, Parallax! We really need these, along with noparse. There are old posts that are still broken without these!
or: https://www.theverge.com/tldr/2018/3/14/17119388/pi-day-pie-math-tau-circle-constant-mathematics-circumference-diameter-radius-holiday-truth
It's OK. As Phil said π is a "normal" number. So π contains τ, τ contains π...
But Phil, so what if the one little area formula needs a extra 2 in it?
https://news.ycombinator.com/item?id=913028
-Phil
Why do you say only their binary expansions?
Surely we expect this be true no matter what base one is using?
I suggest that if π is "normal" then π contains τ, τ contains π, π contains τ... recursively, forever...
As well as everything else one can imagine.
Gotta love Cantor.
-Phil
1) Why does a change of base make any difference to the argument? It's just different notation for the same thing.
2) What is the difference between "finite sequences -- of any length" and an infinite sequence? Surely "any" allows the infinite also?
OK, we may have to account for Cantor's countably infinite and other bigger infinities. But hey, we are talking about a transcendental number here which is suspected to be "normal". How big can a thing be?
But, all this must be speculation. As you said it is not proven that PI is a "normal" number. So surely we don't know.
3
1
4
1
5
9...
Never seen a Tau key.
From the Verge article: "The thing is, we don’t actually use diameter to describe circles."
The thing is, we _do_ use diameter to describe circles. Probably 100:1. Drill bits, hockey pucks, celestial bodies, bullet calibers, rocket fairings, welding rods, cake pans, pie plates (can't forget that!), you name it; if it's round, it's nearly always specified in terms of diameter.
BTW, K2's newest Pi appeared on the doorstep on Pi Day. Today it got Stretched. It's simply mind-blowing what happens when you mix those two. It's the Kinepak of the computer world.
Not quite. In a normal number, any finite sequence can be found with equal probability to any other sequence of the same length. So the probability of finding any random infinite sequence is zero. If the infinite decimal expansion of tau existed in the infinite decimal expansion of pi, so would 111111111... . But then pi would rational. But it's not.
-Phil