It's Pi Day, so I thought I would have some fun with numbers, while also revisiting a very old argument about the nature of numbers I've written about before.

The mathematical constant Pi, the ratio of any circle's circumference to its diameter, has fascinated people for millennia. The fact something infinite (& whose numbers don't repeat over the infinite) is derived from something as simple as a circle, is in many respects a "beautiful" yet complex feature of the universe. And did I mention we still don't understand everything about it? If you then throw in Euler's Identity, and how Pi connects to other fundamental concepts of math & science, you start to understand why 3.141593... has fascinated people for a very long time.

But what are Pi, 0, 1, or for that matter, numbers in general? Here's a nice little mind-bender that's been around for a while: Is mathematics a human invention, or a discovery made by humanity? It seems like a simple question, but not quite.

From CNN:

The sound of meditation for some people is full of deep breaths or gentle humming. For Marc Umile, it's "3.14159265358979..."... "There are many things that could not be built without implementing the constant pi," Umile said. "The great engineering marvels like the arch or suspension bridges we cross over, the tunnels spanning within mountains or even under the water that we drive through. ... Without it, everything would be incomplete or in danger of collapse."

Designing any structure with cylindrical components involves pi, as the formula for area is pi multiplied by the square of the radius... Mathematicians know that pi is irrational -- it cannot be represented as one number divided by another -- and transcendental, meaning it is not algebraic. That means, theoretically, that its digits will continue on indefinitely without ending in repetition -- in other words, the digits won't suddenly continue infinitely as 5s after 3 trillion digits (Pi's digits were calculated out to a record 2.7 trillion places in December by French computer scientist Fabrice Bellard).

That also means, mathematicians theorize, that any string of numbers you can imagine is somewhere in pi -- for instance, look for your birthday. Coincidentally, "360," the number of degrees in a circle, occurs at digits 358 to 360.

On the other hand, the true "randomness" of pi's digits has never been proven, which is frustrating, said David Bailey, a technologist at Lawrence Berkeley National Laboratory who is still working on this question. "For all we know, just out beyond where we calculated, there are no more 5s," he said.

Wikipedia has a rough history of the computation of Pi.

The earliest evidenced conscious use of an accurate approximation for the length of a circumference with respect to its radius is of 3+1/7 in the designs of the Old Kingdom pyramids in Egypt. The Great Pyramid at Giza, constructed c.2550-2500 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π. Egyptologists such as Professors Flinders Petrie and I.E.S Edwards have shown that these circular proportions were deliberately chosen for symbolic reasons by the Old Kingdom scribes and architect. The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2600 BC. This application is archaeologically evidenced, whereas textual evidence does not survive from this early period.

That the ratio of the circumference to the diameter of a circle is the same for all circles, and that it is slightly more than 3, was known to Ancient Egyptian, Babylonian, Indian and Greek geometers. The earliest known textually evidenced approximations date from around 1900 BC; they are 25/8 (Babylonia) and 256/81 (Egypt), both within 1% of the true value. The Indian text Shatapatha Brahmana gives π as 339/108 ≈ 3.139.

Archimedes (287–212 BC) was the first to estimate π rigorously. He realized that its magnitude can be bounded from below and above by inscribing circles in regular polygons and calculating the outer and inner polygons' respective perimeters... The average of these values is about 3.14185... Around AD 265, the Wei Kingdom mathematician Liu Hui provided a simple and rigorous iterative algorithm to calculate π to any degree of accuracy. He himself carried through the calculation to a 3072-gon and obtained an approximate value for π of 3.1416. Later, Liu Hui invented a quick method of calculating π and obtained an approximate value of 3.14 with only a 96-gon, by taking advantage of the fact that the difference in area of successive polygons forms a geometric series with a factor of 4.

Around 480, the Chinese mathematician Zu Chongzhi demonstrated that π ≈ 355/113, and showed that 3.1415926 < π <3.1415927 using Liu Hui's algorithm applied to a 12288-gon. This value would remain the most accurate approximation of π available for the next 900 years. </p>

And then there is Euler's Identity:
Derived in the 18th century by Swiss mathematician and physicist Leonhard Euler, the equation "connects" multiple fields of mathematics. I once had a professor who jokingly called it proof of "spooky order" in the universe.

Euler's identity is considered by many to be remarkable for its mathematical beauty. Three basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:

• The numbers 0 and 1, [which serve double purposes as both standard integers and constants. The number 1 serves as a numeral under addition and subtraction, but as a constant under multiplication, addition, or exponentiation. This latter idea can be understood by realizing that any number or variable can be defined as itself multiplied by 1. 0 on the other hand is a very useful, multipurpose constant which can be used in countless algebraic capacities].
• The number π, which is ubiquitous in trigonometry, geometry of Euclidean space, and mathematical analysis (π ≈ 3.14159).
• The number e, the base of natural logarithms, which also occurs widely in mathematical analysis (e ≈ 2.71828).
• The number i, imaginary unit of the complex numbers, which contain the roots of all nonconstant polynomials and lead to deeper insight into many operators, such as integration.

But what are numbers?

Let's start with a "simple" truth... at least in base 10.

Now, on one level, it's a fundamental truth of existence. It should be true within this universe, whether humanity is here to know it or not. It should be as true today as it was 10,000 years ago. And it should be as true here on Earth as it would be if you were floating somewhere in the Eagle Nebula, 7,000 light years away. And so far no one has "invented" a way to make 2+2=5 & still have it make any kind of sense.

On the other hand, what are "2" & "4"? Mathematics has sometimes been described as the language of science & as such could be described as a tool. Mathematical concepts are not observable. A pulsar, Earth's atmosphere, a certain species of frog, all exist in nature as observable things to study within an empirical framework. The number "1" only exists as a human construct on a piece of paper, classroom board, or computer screen. It's a symbolic representation of an idea used to express other ideas, just like +, -, $, %, and even the period I'm going to end this sentence with right now. And if that wasn't enough, all of this leads to Plato & a very old debate about the nature of mathematics. Discovery or invention? Those who espouse discovery note that mathematical statements are true or false regardless of personal beliefs, suggesting that they have some external reality. But this leads to some odd notions. Where, exactly, do these mathematical truths exist? Can a mathematical truth really exist before anyone has ever imagined it? [...]Plato is the standard-bearer for the believers in discovery. The Platonic notion is that mathematics is the imperturbable structure that underlies the very architecture of the universe. By following the internal logic of mathematics, a mathematician discovers timeless truths independent of human observation and free of the transient nature of physical reality. "The abstract realm in which a mathematician works is by dint of prolonged intimacy more concrete to him than the chair he happens to sit on," says Ulf Persson of Chalmers University of Technology in Sweden, a self-described Platonist. However, Plato has his detractors. If the mathematical ideas are out there, waiting to be found, then somehow a purely abstract notion has to have existence even when no human being has ever conceived of it. Because of this, [Barry] Mazur, [a mathematician at Harvard University] describes the Platonic view as "a full-fledged theistic position." It doesn’t require a God in any traditional sense, but it does require "structures of pure idea and pure being," he says. Defending such a position requires "abandoning the arsenal of rationality and relying on the resources of the prophets." Indeed, Brian Davies, a mathematician at King's College London, writes that Platonism "has more in common with mystical religions than with modern science." And modern science, he believes, provides evidence to show that the Platonic view is just plain wrong. He titled his article "Let Platonism Die." A pretty simple way to resolve this would be to say it's both a discovery & an invention, but that would be too easy & rob people of thousands of years of arguing. #### Originally posted to 医生的宫殿 on Sun Mar 14, 2010 at 10:03 PM PDT. #### Tags EMAIL TO A FRIEND X Your Email has been sent. 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Are you sure you want to save these changes to the published diary? #### Comment Preferences #### 336comments | Permalink • ##### The BEST tip jar EVER!(175+ / 0-) Recommended by: pontificator, Pat K California, Yosef 52, benr, deben, Rimjob, mndan, TrueBlueMajority, BigOkie, Heather in SFBay, bronte17, MillieNeon, mrblifil, sidnora, wader, tomephil, TexDem, NYFM, Tillie630, AbsurdEyes, Oaktown Girl, side pocket, bablhous, carlos the jackal, Jersey Joe, Julie Gulden, tergenev, historys mysteries, blueyedace2, LarisaW, BCO gal, Luetta, Simplify, truong son traveler, basquebob, MT Spaces, reflectionsv37, cfk, John DE, skyounkin, peteri2, Phil S 33, Churchill, sunbro, Pluto, debedb, Mother Mags, Paul Ferguson, keefer55, Liberal Protestant, Patriot Daily News Clearinghouse, Krush, HoundDog, mr crabby, Hobbitfoot, JVolvo, bernardpliers, Unitary Moonbat, Helpless, profh, Clive all hat no horse Rodeo, frankzappatista, Statusquomustgo, crystal eyes, ipsos, AllanTBG, Pandoras Box, Aaa T Tudeattack, DBunn, tegrat, One Pissed Off Liberal, dotsright, dmh44, desertguy, Cottagerose, possum, bigjacbigjacbigjac, yoduuuh do or do not, blue71340, unionboy, txlosthorn, davehouck, kingyouth, Seneca Doane, rainmanjr, MI Sooner, jnhobbs, millwood, ValleyForger, Rumarhazzit, Desa, TomP, Empower Ink, cville townie, gizmo59, VA Breeze, kafkananda, Dem in the heart of Texas, JayC, mconvente, swampus, flowerfarmer, Louisiana Fiddle Gal, ferment, NotGeorgeWill, ms scarlett leadpipe, Involuntary Exile, Cassandra Waites, kyril, ptolemynm, psilocynic, palantir, shortgirl, LaFeminista, 207wickedgood, maggiejean, cameoanne, SciMathGuy, 1BQ, rubyclaire, J M F, Neon Vincent, cantelow, bsmechanic, Michael James, be the change you seek, janmtairy, pvlb, cn4st4datrees, mkor7, MySobriquet, allep10, blueocean, louisprandtl, Bene Gesserit1, ohmyheck, ratmach, Just Bob, marabout40, KroneckerD, Obamican08, veracityus, RethinkEverything, blueyescryinintherain, Interceptor7, Lost and Found, CrissieP, puffmeister, TKO333, ThirtyFiveUp, Unenergy, alethea, Otteray Scribe, bvig, cany, NellaSelim, freesia, m00finsan, Seitanist, elektra, Billdbq, Shes a Riot, dle2GA, MKHector, IL JimP, enhydra lutris, MuskokaGord, yaque, The YENTA Of The Opera, Archie2227, bloomin, PrometheusUnbound, TrapperSF, nutbutter, sjterrid Thank you! "Let reverence for the laws . . . become the political religion of the nation." ~ Abraham Lincoln [ Parent ] • ##### Posted this in the OND tonight(29+ / 0-) A Brief History of Pi by Sarah Jacobsson Everybody knows that the value of pi is 3.14...er, something, but how many people know where the ratio came from? Actually, the ratio came from nature--it's the ratio between the circumference of a circle and its diameter, and it was always there, just waiting to be discovered. But who discovered it? In honor of pi day, here's a brief (sort of) history of how pi came to be known as 3.14(159265358979323846264338327950288 The current record for the number of is 2.7 trillion digits. If the US only had a dollar for each one! and I found this interview with the previous record holder for the number of digits computed for Pi. Interview with the Japanese researcher who found 2.5 Trillion digits of Pi Of course there's the Wiki: Pi And a suggestion for a more properly defined day of Pi Yum! I just love π • ##### Hey, Rimjob...(12+ / 0-) I wanna take a math class from your math instructor up above in your diary's chalkboard photo. Man, I'd be learning theorems ALL DAY LONG. -4.75, -5.33 Cheney 10/05/04: "I have not suggested there is a connection between Iraq and 9/11." [ Parent ] • ##### I feel like a cat. I could watch that forever.(17+ / 0-) Health Care for Profit. More Profit less Health Care. [ Parent ] • ##### so i have a question: (11+ / 0-) Is there any reasonable way in mathematics, aside from by twisting definitions, that an infinity can be a subset of an integer? Reason I ask is, my thought on that is that it can't, and that this makes a useful example to cite by way of demonstrating that one can't have unlimited economic growth (a set of infinities) on a finite planet (whose relevant characteristics are denominated in integers). Feel free to tell me I've been making a stupid fool of myself if I'm wrong; I'm not ego-attached to these things; as with science, what matters is to get the facts right and draw supportable conclusions. • ##### One black hole . . .(2+ / 0-) Recommended by: G2geek, mkor7 can contain an infinite amount of matter. Does that count? Seriously, great question. I'd be curious to hear a more informed answer. • ##### I don't think that's strictly true(6+ / 0-) we can pretty much determine the mass of a black hole and there are micro black holes that certainly don't contain an infinite amount of matter • ##### Oh well . . .(2+ / 0-) Recommended by: G2geek, palantir figured it was worth a shot. The universe itself has a fixed mass, correct? So even there one universe would not contain an infinity. • ##### "One infinity" is an example of....(1+ / 0-) Recommended by: palantir ....playing tricks with the concepts. It is also the case that if you enumerate universes, then a single infinite universe is a subset of a potentially infinite number of universes. But here we are concerned with denominators. One can't reasonably compare e.g. a finite quantity of barrels of oil with an infinite quantity of stars in a universe. What I'm asserting is that when the denominators are the same, the numerators follow the rule that an infinity exceeds any integer by some unknown amount. • ##### you can't pick a biggest number(6+ / 0-) 'cause I got one that's bigger. • ##### And don't forget(1+ / 0-) Recommended by: Leo in NJ some infinities are bigger than other infinities. Warning: Erwin Schroedinger will kill you like a cat in a box. Maybe. [ Parent ] • ##### i don't know if we know the answer to that.(0+ / 0-) • ##### see wiki(0+ / 0-) • ##### No it can't(0+ / 0-) • ##### I'm not sure I understand your question(2+ / 0-) Recommended by: G2geek, kyril I'm reading it to mean, is a single number a superset of infinity. • ##### interesting way of putting it. (1+ / 0-) Recommended by: carlos the jackal If one puts it that way, clearly the answer also has to be No, and we're convergent. Whatever single number one names as the superset, the subset has to be a smaller quantity. What I've been trying to do with this one, is to come up with a minimalistic logical representation of the empirical fact that unlimited growth is never possible within a finite system. For example the economy is the subset, the Earth itself is a superset that contains the economy. The Earth is a Euclidean solid, so it is by definition (as well as by observation) finite. Thus any subset of the Earth must also necessarily be finite: and as a consequence, its growth must and will at some point cease. This is true for the economy, and this is true for the population of any species. If I've somehow screwed up the concept due to lack of training in mathematics, I'd certainly like to hear about that so I can stop saying foolish things. That was the basis of my inquiry here. • ##### Hmmm, I think I understand what you are saying. (1+ / 0-) Recommended by: kyril I'm not sure there's a simple way to make it stick. The earth is not necessarily a closed system and as such, there is possibility of infinite growth based on human and the earth's interactions with forces outside of the planet. If the earth were to be a perfectly closed system, then there's going to be limited resources, which in turn would mean there can't be infinite growth. open your mind or someone else will open it for you, but be careful you don't open it too much for you brain to fall out. [ Parent ] • ##### not on the surface of Earth there isn't. (0+ / 0-) The potential for "infinite growth" only exists off Earth. Once we're in space, there is no hard limit in any meaningful sense. But so long as we're stuck to the surface of a Euclidean solid, we have a finite surface area and finite mineral resources to work with. The effectively limitless energy supply from the Sun doesn't change that. • ##### There is always the Sun(2+ / 0-) Recommended by: G2geek, kyril and the rest of the solar system. There are vast amounts of energy available from solar radiation and a great amount of resources in the solar system. The asteroid belt alone contains tremendous wealth. This means that we need to become a space faring civilization. If we choose to remain bound to Earth then I would guess that mean an end to unlimited growth. Of course, the universe is finite so no growth curve can ever be truly infinite. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### yes and yes. (1+ / 0-) Recommended by: SoCaliana Though, to become a truly spacefaring civilization requires that we achieve sustainability on Earth. We have to accept living within our limits here or we will never be able to go there in any meaningful sense. This is a paradox similar to addiction, and also similar to emotional maturity in a general sense: for a person to have something they want, they have to give up behaving as if they want it more than anything else in the world. Beyond which, "growth" is a meaningless concept in terms of human wellbeing. "More" does not equal "better." For the price of doing Iraq we could have gotten to Mars once. We just burned through something like three trillion dollars bailing out a bunch of petulant sociopaths on Wall Street: and for that sum of money we could have built a program of multiple human missions to Mars. We have been squandering our everything on the most insane, stupid, self-destructive and self-defeating exercises in wanton waste, and meanwhile Mars and the stars are as far from human touch as they were almost a century ago when we squandered our everything into the meat grinder of trench warfare. The underlying reality is: the humans must evolve. Then we will have Mars, the stars, and the cosmos. Otherwise, we will likely become extinct within two centuries. • ##### No argument about us squandering(0+ / 0-) our resources. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### A convergent geometric series(6+ / 0-) For example the set 1/2, 1/4, 1/8, 1/16, ... which has an infinite number of members, but their sum is bounded by 1. More you add, closer to 1 you get. Of course, if our economic growth was a convergent geometric progression we'd eventually have to settle with such news stories as "the economy grew one billionth of a cent last year." But no recessions! I knew a professor who liked to start the first lecture of relevance to this topic by bringing a slice of cake and handing it to the student at one end of the first row of seats, with the instruction to eat half and pass it along to the next person who would eat half of the remaining portion, and so on. He assured the class there would be some for everyone - and of course some left for a second round. Perhaps one bonus of this illustration was to annoy those who always sat at the back. • ##### interesting point, i'll have to give this....(0+ / 0-) more thought. What you're describing is an asymptote. An asymptotic curve can get infinitely closer to a destination point, by infinitely smaller degrees, but never quite reach it. So one could have an infinity of points on an asymptotic curve reaching a given number. At one level that would seem to make mush out of my attempt at a simple formulation of the issue of growth on a finite planet. At another level, we see the asymptote in action, in areas such as the rise of intellectual property fascism: the attempt to wring one more penny and one more fraction of a penny, on ad infinitum, from an economy that has for all practical purposes hit the limits in terms of extractable and convertible physical resources. This definitely deserves more thought. -- Your professor had a clever illustration there, but it would have had another side effect: spreading contagious diseases from one dirty hand to another mouth, to another dirty hand to another mouth, all the way around. By the time a few crumbs reached the back of the class, they would have been infested with all manner of nasties including the fecal coliform of anyone who didn't wash their hands after their last bowel movement. I suppose if someone brought Norovirus to class, this would also have illustrated the principle of rapid population collapse. • ##### If you try to stuff infinitely many pigeons...(4+ / 0-) ...into only finitely many pigeonholes, then at least one pigeonhole will house infinitely many pigeons. Not sure if this answers your question though. I just happen to like the principle involved. • ##### Love that line BTW. That would imply pure maths (3+ / 0-) Recommended by: G2geek, kyril, pigeonhole principle is nothing. Not sure a lot of pure mathematicians would agree with you....lol open your mind or someone else will open it for you, but be careful you don't open it too much for you brain to fall out. [ Parent ] • ##### I look at it as a representation problem.(3+ / 0-) Recommended by: carlos the jackal, G2geek, kyril If a piece of mathematics is representable (definable? interpretable?) in the ultimate mathematical structure that is "reality", then that piece of mathematics is applied. If no such representation exists for that piece of mathematics in "reality", then that piece mathematics is pure. Distinguishing between the two from inside of "reality" is a somewhat nontrivial task...lol everything is applied mathematics the rest is pure mathematics [ Parent ] • ##### but you can't get infinitely many pigeons...(1+ / 0-) Recommended by: pigeonhole principle ...into a pigeonhole, or they will become ex-pigeons or former pigeons along the way. And if you keep stuffing, then eventually they will achieve a critical mass where the pigeonhole will become a black hole and suck you in along with the former pigeons. • ##### There are an infinite number of integers(7+ / 0-) Each with an infinite number of real numbers between them. As information becomes a thing of value, your real question is: are there an infinite number of valuable ideas? By language theory we know that expressing an idea requires a certain number of pieces of information, and representing that information requires some medium, so I would argue, "no". However, I am reminded of a joke: To torment two inhabitants of hell, an engineer and a mathematician, Satan placed them at the end of a long hallways. At the other end was a beautiful succubus disporting herself. Satan said "When I give the signal, you may run half the distance between your current position and that of the succubus". Satan signaled, and the engineer eagerly ran, while the mathematician did not run. Satan looked at the mathematician with ire. "Why did you not run?" he inquired. "Because I'll never reach her" came the reply. Satan looked at the engineer and said "Come back. Your friend has discerned my trick. You do not need to play any longer." The engineer replied "No, I wish to continue playing. Sooner or later I'll be close enough for all practical purposes." My point being, that while we may not be able to have infinite economic growth, we may be able to continue to grow at an exponential rate for the expected lifetime of mankind - that is, for all practical purposes. In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra [ Parent ] • ##### That is hilarious!(2+ / 0-) Recommended by: G2geek, kyril Unapologetically pro-citizen. Not anti-corporation just very pro-citizen. [ Parent ] • ##### me being an engineer...(2+ / 0-) Recommended by: mn humanist, blue aardvark ...and gay.... I'd take the mathematician. • ##### In fact, there are more real numbers between...(1+ / 0-) Recommended by: kyril ...0 and 1 than there are integers. Some sets are more infinite than others. There are an infinite number of integers Each with an infinite number of real numbers between them. everything is applied mathematics the rest is pure mathematics [ Parent ] • ##### Some infinities contain an infinite number(1+ / 0-) Recommended by: pigeonhole principle of smaller infinities. In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra [ Parent ] • ##### Every infinity contains an infinite number...(0+ / 0-) ...of infinite copies of the same size as itself. everything is applied mathematics the rest is pure mathematics [ Parent ] • ##### I'm assuming that we are talking about cardinal..(0+ / 0-) ...numbers here, not ordinal numbers or something. everything is applied mathematics the rest is pure mathematics [ Parent ] • ##### How true...(0+ / 0-) And apropos to the topic: For the mathematician, Pi is 3.14159... For the engineer, Pi is "a little more than 3". • ##### Did you know?(1+ / 0-) Recommended by: mn humanist That infinity doesn't exist in nature. That a perfect circle, square, rectangle, isosceles triangle, etc. -- concepts that us human beings can grasp with ease -- do not exist in manifested form in this universe? • ##### when you use elipsis(3+ / 0-) to indicate an incompletely expressed number (as you do in the 2nd paragraph) the portion of the number preceeding the elipsis should be truncated, not rounded . . . Fake Left, Drive Right . . . not my idea of a Democrat . . . [ Parent ] • ##### Thank you(0+ / 0-) That was bothering me too. Every horror committed by man begins with the lie that some man is not a man. - Jyrinx [ Parent ] • ##### and what is with this fixation(0+ / 0-) with the ratio of the circumfrence to the diameter? Why not the ratio of the diameter to the circumfrence? That's what's wrong with the animation in your tip jar . . . it is not "counting" anything. Each of the numbered lines should represent one complete rotation of the wheel . . . I leave it to you to figure out where that silly "pi" thing would then fall . . . It all goes wrong from the beginning when you start with linear thinking . . . Fake Left, Drive Right . . . not my idea of a Democrat . . . [ Parent ] • ##### You are late(17+ / 0-) pi Day was yesterday in China and you did not post in time to catch our celebration. We had a killer Mathaletes party full of fun, drink and of course, many flavors of pi. You punishment - you must memorize the following sequence of numbers by Saturday when you WILL BE TESTED 3.1415926535897932384626433832795028 84197169399375105820974944592307816 40628620899862803482534211706798214 80865132823066470938446095505822317 25359408128481117450284102701938521 10555964462294895493038196442881097 56659334461284756482337867831652712 01909145648566923460348610454326648 21339360726024914127372458700660631 55881748815209209628292540917153643 67892590360011330530548820466521384 14695194151160943305727036575959195 30921861173819326117931051185480744 62379962749567351885752724891227938 18301194912983367336244065664308602 13949463952247371907021798609437027 70539217176293176752384674818467669 40513200056812714526356082778577134 27577896091736371787214684409012249 53430146549585371050792279689258923 54201995611212902196086403441815981 36297747713099605187072113499999983 72978049951059731732816096318595024 45945534690830264252230825334468503 52619311881710100031378387528865875 33208381420617177669147303598253490 42875546873115956286388235378759375 19577818577805321712268066130019278 76611195909216420198938095257201065 48586327886593615338182796823030195 20353018529689957736225994138912497 21775283479131515574857242454150695 95082953311686172785588907509838175 46374649393192550604009277016711390 09848824012858361603563707660104710 18194295559619894676783744944825537 97747268471040475346462080466842590 69491293313677028989152104752162056 96602405803815019351125338243003558 76402474964732639141992726042699227 96782354781636009341721641219924586 31503028618297455570674983850549458 85869269956909272107975093029553211 65344987202755960236480665499119881 83479775356636980742654252786255181 84175746728909777727938000816470600 16145249192173217214772350141441973 56854816136115735255213347574184946 84385233239073941433345477624168625 18983569485562099219222184272550254 25688767179049460165346680498862723 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573952311342716610213596953623144295 248493718711014576540359027993440374 200731057853906219838744780847848968 332144571386875194350643021845319104 848100537061468067491927819119793995 206141966342875444064374512371819217 99983910159195618146751426912397489 409071864942319615679452080951465502 252316038819301420937621378559566389 377870830390697920773467221825625996 615014215030680384477345492026054146 659252014974428507325186660021324340 8819071048633173464965145390579626856 100550810665879699816357473638405257 145910289706414011097120628043903975 951567715770042033786993600723055876 317635942187312514712053292819182618 612586732157919841484882916447060957 527069572209175671167229109816909152 801735067127485832228718352093539657 251210835791513698820914442100675103 346711031412671113699086585163983150 197016515116851714376576183515565088 490998985998238734552833163550764791 853589322618548963213293308985706420 467525907091548141654985946163718027 098199430992448895757128289059232332 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775687900290951702835297163445621296 404352311760066510124120065975585127 617858382920419748442360800719304576 189323492292796501987518721272675079 812554709589045563579212210333466974 992356302549478024901141952123828153 091140790738602515227429958180724716 259166854513331239480494707911915326 734302824418604142636395480004480026 704962482017928964766975831832713142 517029692348896276684403232609275249 603579964692565049368183609003238092 934595889706953653494060340216654437 558900456328822505452556405644824651 518754711962184439658253375438856909 411303150952617937800297412076651479 394259029896959469955657612186561967 337862362561252163208628692221032748 892186543648022967807057656151446320 469279068212073883778142335628236089 632080682224680122482611771858963814 091839036736722208883215137556003727 983940041529700287830766709444745601 345564172543709069793961225714298946 715435784687886144458123145935719849 225284716050492212424701412147805734 551050080190869960330276347870810817 545011930714122339086639383395294257 869050764310063835198343893415961318 543475464955697810382930971646514384 070070736041123735998434522516105070 270562352660127648483084076118301305 279320542746286540360367453286510570 658748822569815793678976697422057505 968344086973502014102067235850200724 522563265134105592401902742162484391 403599895353945909440704691209140938 700126456001623742880210927645793106 579229552498872758461012648369998922 56959688159205600101655256375679 ... Ask me about my daughter's future - Ko [ Parent ] • ##### whatever!(4+ / 0-) • ##### i already memorized those(9+ / 0-) what are the next few? :-D "Politics is like driving. To go backward put it in R. To go forward put it in D." --Tom Harkin [ Parent ] • ##### Sorry(5+ / 0-) Scoop does not support text records of that length. Follow my instructions: (1) Go to a big box store. (2) Buy 10 cases of toilet paper, 2 rolls of scotch tape and 100 ink cartridges for your printer (3) Push out the toilet paper cores and tape the ends of one roll to the begining of the next roll untill they are connected as one continious strip. Load in your printer. (4) Log on to the internet and download the linked Zip file here (5) Decompress and install the software. (60 Run the program and print the results until the paper is exhuasted. (7) Skip the first 10,000 digits and start memorizing. #8^o> Ask me about my daughter's future - Ko [ Parent ] • ##### tl;dr(3+ / 0-) Recommended by: koNko, kyril, m00finsan nt It's the economy, stupid! [ Parent ] • ##### What a great explanation of pi !!!(3+ / 0-) That tip jar is AMAZING!! They only call it class war when we fight back! ht: buhdydharma [ Parent ] • ##### I thought your title(8+ / 0-) was a reference to Spinal Taps wee tiny Stone Henge. But this is good too. • ##### May I use this animated gif? (nt)(3+ / 0-) Recommended by: Rimjob, TrueBlueMajority, kyril The Big Lie is this: That there is not enough to go around. [ Parent ] • ##### i already stole it n/t(2+ / 0-) Recommended by: Rimjob, kyril "Politics is like driving. To go backward put it in R. To go forward put it in D." --Tom Harkin [ Parent ] • ##### Go Right Ahead......(1+ / 0-) Recommended by: kyril I "borrowed" it from Pi's Wikipedia page. :) • ##### What's really sad(2+ / 0-) Recommended by: Rimjob, kyril is that I missed being tipper #355 by ><that much.</p> "A riot is an ugly thing . . . and I think it is just about time we had one!" -- Inspector Kemp, Young Frankenstein [ Parent ] • ##### Nice slide rule! n/t(2+ / 0-) Recommended by: Rimjob, kyril Float like a manhole cover, sting like a sash weight! Clean Coal Is A Clinker! [ Parent ] • ##### Meanwhile, on Redstate(9+ / 0-) they're probably debating whether Jesus would have liked Glock or Smith & Wesson better. • ##### um ...(2+ / 0-) Recommended by: Rimjob, m00finsan Ask me about my daughter's future - Ko [ Parent ] • ##### Happy Pi Day!!(1+ / 0-) Recommended by: Rimjob ((Rimjob)) Every horror committed by man begins with the lie that some man is not a man. - Jyrinx [ Parent ] • ##### BTW, i, mathematically, is...(4+ / 0-) Recommended by: Rimjob, mn humanist, kyril, m00finsan ...the square root of negative one. At least it was while I was in college. Although it is sometimes represented by j, such as in electrical engineering, since i represents current in EE. The sleep of reason produces monsters. [ Parent ] • ##### Yes, it is(3+ / 0-) Recommended by: Alumbrados, Rimjob, m00finsan and e^(i*pi) = -1 Every horror committed by man begins with the lie that some man is not a man. - Jyrinx [ Parent ] • ##### I Like It Better With The Zero.....(3+ / 0-) Recommended by: Alumbrados, kyril, m00finsan From Physics World: One of the most frequently mentioned equations was Euler's equation, e^{i \pi} + 1 = 0. Respondents called it "the most profound mathematical statement ever written"; "uncanny and sublime"; "filled with cosmic beauty"; and "mind-blowing". Another asked: "What could be more mystical than an imaginary number interacting with real numbers to produce nothing?" "Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don't know what it means. But we have proved it, and therefore we know it must be the truth." Benjamin Peirce, on Euler's Identity • ##### Question(0+ / 0-) for a non mathematician. Is it not a fact that the rolling circle lands at the exact place every 360 degree revolution. And if so, does that not indicate that pi eventually would calculate out to a final number? "Whenever I get the urge, I lie down 'til it passes." - Mark Twain on exercise. [ Parent ] • ##### Yes on 1, no on 2(1+ / 0-) Recommended by: Rimjob The measure a rolling circle traveling in a 360 degree revolution is the circle's circumference. Pi is the ratio of this circumference to the circle's diameter. • ##### there are no perfect circles(0+ / 0-) and if space is quantized it may not even be possible to construct a perfect circle, so a real circle won't land on the exact same spot. • ##### Ummm.. Citation, plz?(0+ / 0-) • ##### For which part?(1+ / 0-) Recommended by: mkor7 That something made of discreet (atomic) elements can't be a perfect circle or that this could also apply to space? The first is self evident from a simple thought experiment... arrange 3 elements into a "ring" and you have a triangle, add one and you have a square, another a pentagon. How many do you have to add before it stops being a "polygon that approach a circle" and starts being a circle? The second is tied up in plank scale physics and quantum gravity. I can't give you a simple cite but you can Google "discrete units of space quantum gravity" (without quotes) and explore from there. • ##### Fascinating(0+ / 0-) and mind blowing. Thanks to you and all who offered answers to my question "Whenever I get the urge, I lie down 'til it passes." - Mark Twain on exercise. [ Parent ] • ##### μή μου...(20+ / 0-) μή μου τούς κύκλους τάραττε Because of people like Sarah Palin we need the word retarded to explain what's happening in America - Bill Maher • ##### Uhm.(13+ / 0-) Quit that. :P Lack of preparation on your part does not constitute an emergency on mine. [ Parent ] • ##### That has to mean(14+ / 0-) Kos has gone socialist, we are using the font! "Come, come, my conservative friend, wipe the dew off your spectacles, and see the world is moving." Elizabeth Cady Stanton [ Parent ] • ##### hold on now. i can make MY pi out of anything(2+ / 0-) Recommended by: bigjacbigjacbigjac, psilocynic I want, absent change. So, you were saying...? 866-338-1015 toll-free to Congress in D.C. USE it! You can tell how big a person is by what it takes to discourage them. [ Parent ] • ##### My translation . . .(8+ / 0-) via one source renders: "The dictionary did not find any matching words". A more personalized translation might be: "I took one semester of ancient Greek and barely passed. I know enough to recognize it when I see it, but I don't know enough to know what it actually means". Finally, Google The Great returns: "Do not disturb my circles" -- Archimedes. The last words attributed to Archimedes are "Do not disturb my circles" (Greek: μή μου τούς κύκλους τάραττε), a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. • ##### and according to mathematicians, the most(0+ / 0-) significant contribution the Romans ever made to mathematics was the day they killed Archimedes. Hard to imaggine them doing all that engineering with that unbelievably stupid numeral system they were stuck with. Fear is the mind-killer - Frank Herbert, Dune [ Parent ] • ##### Pie(21+ / 0-) Refers to the ratio of the outside crust to a single slice. • ##### So are your slices big or ...? nt(1+ / 0-) Recommended by: bigjacbigjacbigjac 866-338-1015 toll-free to Congress in D.C. USE it! You can tell how big a person is by what it takes to discourage them. [ Parent ] • ##### I admit it: I am a math nerd!(34+ / 0-) OMG! I was an English major in college (with a minor in Medieval History -- to improve my chances at paying employment) . . . but OMG, I just loved algebra . . . the simplicity, the beauty, the ONE ANSWER. It was amazing. And that tip jar, dear Rimjob . . . a thing of beauty. As is PI. "Let reverence for the laws . . . become the political religion of the nation." ~ Abraham Lincoln • ##### Yes, but there are many teabaggers(18+ / 0-) who believe that 2 + 2 = 5, so when Fox News backs them up, it must be true. -4.75, -5.33 Cheney 10/05/04: "I have not suggested there is a connection between Iraq and 9/11." • ##### i hope this makes the rec list(20+ / 0-) nice diary Is mathematics a human invention, or a discovery made by humanity? It seems like a simple question, but not quite I think mathematics- it's sort of like a language used to describe nearly mystical things, almost beyond actual comphrension. Well, for me anyway. I like philosophy better than looking at numbers Love truth, but forgive error-Voltaire. • ##### I think mathematics has been/is always there, (3+ / 0-) we just needed/need to find the language to describe it. Having described it, we could/can prove it, use it. "Nobody beats you until you quit." h/t Gemina13 "We come to love not by finding the perfect person, but by learning to see an imperfect person perfectly." [ Parent ] • ##### No, this is just wrong(1+ / 0-) Recommended by: p gorden lippy Mathematics IS the language we use to describe the world. It is a human creation born from human needs. Even logic. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### I'll let my namesake answer that:(6+ / 0-) God made the integers; all else is the work of man. -Leopold Kronecker "I know this defies the law of gravity, but you see, I never studied law." -Bugs Bunny [ Parent ] • ##### according to Einstein, the question of whether(1+ / 0-) Recommended by: KroneckerD mathematics is a human creation or is waiting to be discovered is "a frog and mouse battle among mathematicians." In any event, great diary. Fear is the mind-killer - Frank Herbert, Dune [ Parent ] • ##### Tags updated, with pleasure.(18+ / 0-) Thank you, Rimjob. "Let reverence for the laws . . . become the political religion of the nation." ~ Abraham Lincoln • ##### Yeah, whatever.(13+ / 0-) Where are the scantily-clad humans? :P Lack of preparation on your part does not constitute an emergency on mine. • ##### Great Diary. n/t(8+ / 0-) • ##### You GOTTA put up a poll with PIE as a choice!!!(8+ / 0-) How did you miss that one?! ;-) • ##### I Would.....(11+ / 0-) But I don't want to chance adding it. I had some problems with the HTML coding for this diary. The diary wouldn't let me write superscript (<sup>) for equations, and I can't get rid of the </p> at the end of the "history" blockquote above. I didn't type it, and it doesn't appear in preview, but it's there in post. There's been a change to the coding for the site. About a week ago, I noticed the Daily Kos HTML checker started rejecting hyperlinks with "target="_blank"", which allows links to "pop" into new tabs. • ##### I love all of us living in this giant black box,(16+ / 0-) big, busy lumps of myelin and fat perched on our shoulders, madly trying to figure out what the hell is going on when we have no outside frame of reference. A universe of puzzles for an infinite number of grad students, world without end, hallelujah! ;D • ##### Today pi day(16+ / 0-) and tomorrow the 2053rd anniversary of the assassination of Julius Caesar! All in one week! • ##### March 14, 1592(12+ / 0-) I wonder if 418 years ago, a scholar somewhere got a big kick of the π moment in history: 3.141592? Now if only someone would invent time travel, so we could find out for certain. • ##### The question would be whether they were on...(2+ / 0-) Recommended by: TrueBlueMajority, Magnifico the planet. If they were in a Catholic country, they would have. If they were in a Protestant or Orthodox church country, they would not have celebrated it. (Points for the person who can tell me why!) The GOP: The Party of Failure. Pass it on. [ Parent ] • ##### if you are referring(1+ / 0-) Recommended by: Magnifico to the adoption of the Gregorian calendar, there were even some Roman Catholic areas that did not adopt the new calendar right away. a diary about the mathematical reasons behind the Gregorian calendar would be a fascinating read! i want my points so long as they are not McCain points! "Politics is like driving. To go backward put it in R. To go forward put it in D." --Tom Harkin [ Parent ] • ##### Can I gety a (11+ / 0-) pecan 3.141592? or a key lime 3.141592? or a pumpkin 3.141592? I love 3.141592! "Come, come, my conservative friend, wipe the dew off your spectacles, and see the world is moving." Elizabeth Cady Stanton • ##### tipped and rwrecked for Euler(11+ / 0-) and the square root of minus one Oh no, the dead have risen and they're voting Republican. - Lisa Simpson • ##### Great music,(4+ / 0-) but I love the face of Kate Bush, as well. That is one Bush I really like. I saw a video of her, just a collage of photos, but it showed the corners of her mouth..... Us guys get excited by many things about beautiful women. With Kate, for me, it is the corners of her mouth, and her voice. Down to 6 billion by 2100. Got contraception? [ Parent ] • ##### The corners of her mouth, and the corners of her (0+ / 0-) mind. And the curves too. • ##### She's amazing.(3+ / 0-) Never for Ever and The Dreaming were amazing... A unique and wonderful musician. (Hounds of Love was nothing to sneeze at, either!) Thanks for the great tune! Historic Obama Civil Rights Poster (based on my cover for The Nation magazine) AVAILABLE NOW at www.zenpop.com [ Parent ] • ##### was it true(16+ / 0-) before the big bang? before numbers could have referred to or connoted anything? by what definition of truth was it then true? The cold passion for truth hunts in no pack. -Robinson Jeffers • ##### and what is the meanong of life(11+ / 0-) dontcha know the simple questions are best ;-) Oh no, the dead have risen and they're voting Republican. - Lisa Simpson [ Parent ] • ##### You and Augustine(9+ / 0-) He started out looking for a literal reading of the Bible and got stuck on the very first word, which we usually translate "In the beginning..." Beginning of what? And what was before that? • ##### heh(5+ / 0-) one of the relatively few areas where i find agreement with him... The cold passion for truth hunts in no pack. -Robinson Jeffers [ Parent ] • ##### I once wrote a book,(5+ / 0-) but it will never be published, I write here instead, accepting my blogging here as my body of writing.... Anyway, in my book, I wrote a chapter on my analysis, or exigesis, of the Bible. I wrote six pages on the first three verses. The first phrase, in the beginning, means, in the first place, or at the start of this essay. The next phrase means that ordinary humans created the religious organizations, the 'heavens,' and the Bible, or scriptures, the 'Earth.' And the Bible was confusing and ineffective, 'without form, and void.' And the 'darkness' of misunderstanding was upon the 'face,' or literal reading of the Bible's 'deep' parables. The spirit of curiosity of the people, 'god,' moved over the face of the books, 'the waters.' And the people said, let us explain the parables of the Bible, and bring them into the light of understanding. And they did. But they have not yet. I am the only one I know who understands that the Bible is parables, likely written by non-believer philosophers, similar to myself. I got the idea from a friend in Houston, but he is a believer, so that would twist his reading of the parables. It is very frustrating to me to see that Christians and many other religious people accept the Bible as somehow simply correct, as absurd as that seems to so many of us, while all non-belivers that I know of simply want to throw it in the trash can as worthless fairy tales. I am the only one I know who sees it as a very useful source of philisophical wisdom, and similar to Aesop's fables. Down to 6 billion by 2100. Got contraception? [ Parent ] • ##### "a useful source of philosophical wisdom"(0+ / 0-) actually I believe it is that, also. we only disagree about what source of inspiration led it to be so wise... :-D "Politics is like driving. To go backward put it in R. To go forward put it in D." --Tom Harkin [ Parent ] • ##### what was before the Big Bang? (3+ / 0-) Science and religion, each in their own way, address the question of ultimate origins. So far we have no empirical way to get back beyond a few billionths of a second after the Big Bang. But as a matter of theory, we expect that there will never be a way to get empirical data of any kind from the moment of or the period before the Big Bang. At that point we leave the realm of empirical science and enter the realm of speculation and perhaps of pure faith. Now where I come down on this, is to a recycling universe at-large, that will eventually give rise to another Big Bang and another "universe" in the sense of our universe or some other in which matter and energy take similar or different configurations. The reason being that unique events are highly improbable, so it is more probable that there has been more than one Big Bang in the "overall" history of "the universe plural." And it is also more probable that this situation would continue to repeat indefinitely. This observable universe appears to be a little less than about 14 billion years old. In the big picture view of things, 14 billion years are not that long. Nor do I think our knowledge of spacetime geometry is so complete that we can entirely rule out the possibility that even an indefinite expansion along all currently measurable axes, could somehow loop back upon itself, or even pull forth another universe from its midst. So here's a potentially dumb question: Given a star that appears to be red shifted from Earth due to the apparent expansion of the universe. That red shift indicates a vector: the apparent movement of that star has a clear direction. Will that star appear to have a red shift to an observer who is further along the direction of its vector path? And wouldn't that observer's observation differ according to its own movement? That is, star A appears to be moving away from us in direction Q. Now take another observer on star B that is along the vector path Q but further from Earth than star A. One would think that the observation made from star B would differ from that made on Earth, by virtue of any difference in relative velocity between star A and star B. The only way that an observer on B will see the same red shift in A as we do on Earth, is if B is receding from A along the same vector and at the same velocity, as A is receding from Earth. Thus, star B would be seen to recede from Earth at twice the velocity of star A, and its red shift would be more pronounced as a result. If you stack up enough of these in a row, what you get is that star Z is outside of our local universe because its motion relative to us "exceeds" c (light speed) (per mainstream physics: at that point we have no way of observing star Z, thus it is outside of our local universe). Yet one has to consider the possibility that somewhere beyond star B is another star X that is not moving along the same vector path Q. In that case, an observer on star X will not observe the same red shift in star B as we do from Earth. Conversely, if we assume the universe is completely isotropic and uniform, then we are tempted to believe that the foregoing situation is not possible, and instead, every observer on every star will observe every other star moving away from themselves uniformly. OK, so what's the best current knowledge on all of this? • ##### There is no before the big bang(5+ / 0-) Time is warped, just like space is. We all differ in ways that matter. But we're all the same in the ways that matter most. [ Parent ] • ##### What plf515 said.(1+ / 0-) Recommended by: TrueBlueMajority General relativity covers a lot of this; when a black hole is created, the inside and outside of the black hole have incommensurate ideas of time. "Inside", time is either meaningless or (similar to) that of "outside" before the collapse. But there's (almost certainly) no way to work backwards from inside; the universes are different -- as far as is known, the outer is inaccessible from the inner (and there are good reasons to think that it truly is). • ##### Tarski defined truth in 1933.(2+ / 0-) Recommended by: TrueBlueMajority, Turkana by what definition of truth was it then true? Which was some time after the big bang. • ##### SInce I see no mention of the Public Option(8+ / 0-) I can only assume you are against it. jk tipped and recced. Nice change of pace. "Any plan I sign must include an insurance exchange ... including a public option" President Obama, 7.18.09 • ##### Here are some great resources on these questions:(10+ / 0-) David Valdman: Like geometry’s relationship with truth, reality’s is similar. There are many ways to experience the world. The most obvious is through the senses, where the world evolves through color and sound. Then there is through science—the mind’s eye—the token of a rational being, which illuminates order from chaos. What is to say there is no way entirely through math? We have learned that truth is a relative term: isomorphic structures are indistinguishable; isometric spaces are identical to those living within them; consistent geometries are on equal footing. Are isomorphic realities likewise valid? Our minds and bodies have grown to interpret reality in a certain, non-unique, way. It may be that there exists a most basic, most fundamental reality, of which scientific insights and natural experiences are translations. If such a reality existed, I would imagine it mathematical in nature. There would be no greater spiritual realization for me than to unify this beautiful world through the power of mathematics. Everything physical would disappear as mere fabrications of a deeper reality, independent of space and time. All we have come to know and experience would emerge as an epiphenomenon—a consequence—of pure math. But I could easily be getting ahead of myself. And the axioms on which reality is built may be physically inspired. And Peter Russell: Mathematics on the other hand is purely a creation of the mind. Mathematics is that body of knowledge that is arrived at by pure reason, and does not rely upon any observations of the phenomenal world. It is free from the limitations imposed by the particular way human minds create their experience of the underlying. As such it probably the closest the human mind can come to understanding the thing-in-itself. The only thing that pure mathematics depends upon anything is the notion of distinction. If I experience two apples I am experiencing two phenomena that can distinguished one from the other; I can eat one and keep the other. I can distinguish between the black ink and the white paper of this page. Even in the underlying reality there is distinction; we may not know what the thing-in-itself is really like, but we can measure its separation in the spacetime interval from another thing-in-itself. If there was no distinction in the cosmos, there would be no difference of any kind. No experience whatsoever. The existence of distinction is as undeniable as the existence of experience itself. Dammit, it's time for some poetry! And some news! • ##### Oh really Mr. Smartie Pants?(2+ / 0-) Recommended by: Yosef 52, TrueBlueMajority Like geometry’s relationship with truth, reality’s is similar. There are many ways to experience the world. The most obvious is through the senses, where the world evolves through color and sound. Now for a dose 'o reality: Why is smell so sentimental? One possibility, which is supported by this recent experiment, is that the olfactory cortex has a direct neural link to the hippocampus. In contrast, all of our other senses (sight, touch and hearing) are first processed somewhere else - they go to the thalamus - and only then make their way to our memory center. linkie Pi and color and sound? Huh. 866-338-1015 toll-free to Congress in D.C. USE it! You can tell how big a person is by what it takes to discourage them. [ Parent ] • ##### Math and Animals(2+ / 0-) Recommended by: Yosef 52, TrueBlueMajority According to recent research, it has been shown that many animals grasp basic mathematical functions. Elephants and monkeys are proficient at counting, determining "greater-than" and "less-than" concepts symbolically, and it appears that this is related to specific cells in the brain. Given that these abilities are seemingly hard-wired (and now that we know the region, it was found that Einstein was particularly gifted in this area), it isn't quite the case then that math is purely philosophical, but rather it is a specialized manifestation of consciousness. Every day's another chance to stick it to The Man. - dls. [ Parent ] • ##### That we may have evolved math abilities (1+ / 0-) Recommended by: Yosef 52 in response to some need does not mean that math is somehow "real". The ability to count I guess can be selected for but mathematics itself is still a human creation and not a feature of the universe. Mathematics is a human language. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### But wouldn't ANY intelligent species anywhere(0+ / 0-) develop this language, albeit using symbols created in their own cultures? Doesn't this argue for the universality of mathematics, a sort of pervasive presence in the physical universe's fabric? Dammit, it's time for some poetry! And some news! [ Parent ] • ##### Probably they would(0+ / 0-) I don't buy into the Sapir-Whorf hypothesis. But that still doesn't elevate math's ontological status. We also don't have to look off planet for languages that seriously fuck with our linguistic conventions. Languages where time is not at all linear, where trees are verbs, there are no genders and that have no concepts at all for color or number. It is our intuition that any non-human species would have a science and math that was at least reducible to ours. But we can't prove that. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### New Math(15+ / 0-) The number i, imaginary unit of the complex numbers, which contain the roots of all nonconstant polynomials and lead to deeper insight into many operators, such as integration. Huh. Here I thought i was simply the square root of -1. Now they go and get all fancy on me. Losing often means that you had the courage to take on a difficult cause with an unlikely outcome. ~ James Perry • ##### Awesome!(17+ / 0-) Late night Daily Kos is like nerd porn. • ##### Yeah, Plato was a big BELIEVER, I feel(13+ / 0-) My highly conservative History teachers in senior year of High School - whose three daughters were Hope, Charity and Faith - adored Plato something fierce. I was a Mathematics major in college. With English (primarily Drama studies), Religious studies undeclared minors and a completed regimen of pre-med science courses. I dabbled in possible majors of non-organic Chemistry, then Physics and finally Mathematics because it grounded so much that we see in the sciences, anyway. It's a language and therefore, a construct. Yes, we discover things in nature to help work with our math, but that's observation aiding our movement of theories - plenty of mathematics has nothing to do with currently observable reality, frankly. Plato was a dreamer who didn't like to admit he was one, in the first place. I still imagine him in the cave, even today. "So, please stay where you are. Don't move and don't panic. Don't take off your shoes! Jobs is on the way." • ##### Plato isn't he the one who(6+ / 0-) posted bail for Socrates? Oh no, the dead have risen and they're voting Republican. - Lisa Simpson [ Parent ] • ##### and yet: (2+ / 0-) Recommended by: wader, Lefty Mama Platonic concepts have often proven themselves useful in arriving at hypotheses that accurately describe empirical reality. The human brain is often described in terms of its ability to discern patterns. The debate then arises, as to whether those patterns exist in nature or only in the mind of the observer. Clearly the phenomena so described, do exist in nature. The regularities of orbits of planets around stars and satellites around planets; the self-similarities and scaling phenomena described by chaos theory; and more; all of these exist empirically. What exists in the mind of the observer, is the sense of meaning of the relationships between observables. And this sense of meaning is able to make viable predictions about further relationships, that are supported by further observations. The fact that we can make viable predictions that are supported, is proof of one (or possibly both) of two things: One, that the patterns we perceive are in fact substantive and do in fact describe facts of nature that exist "out there" independently of ourselves. Two, that the only reason we can successfully predict future observations is because they are only further parts of ourselves, our own imaginations, that we have not yet discovered. If we take the anti-Platonic view and hold that the patterns we find in nature and mathematics are purely and only creations of our own mind, then we necessarily end up with a kind of collective solipsism, where the entirety of our observations is also a figment of our minds. Are you quite sure you want to go there? • ##### I haven't attempted an anti-Platonic view,(2+ / 0-) Recommended by: G2geek, susanw so hopefully not a direct issue for me. I just feel that Plato is inadequate in this area, due to his personal biases. I find it limiting to rely purely upon Platonic or formalistic assumptions when it comes to mathematics, actually. There's a happy medium which seems more rational and emotionally fulfilling for my own perspectives. Not all mathematics relates to reality we can describe - in Plato's time, claiming that the mapping of math to physical constructs was an exercise and waving-of-hands claim he could more readily argue and have some heads nodding along in agreement, I feel. Nowadays, you have folks like Kurt Godel who have revealed quite rationally that mathematics need not be axiomatic in its aspects or derivation. Being a constructed language by humans, it might naturally be used to help model our physical reality that is currently observable and even not yet observable, but some of it has no ability to be proven in that same reality. We assume into existence some of our constructs that exist on paper, often so that the internal logic we otherwise utilize can remain consistent within one perspective or another. We like consistency and will make things appear so by various, sometimes tortured (or inspired) means, IMHO. And yet, that's a potentially ephemeral, even artistic notion coming to the fore and even relates to how we use verbal/written language, in all its current and perhaps future forms. It's can and does go beyond describable purpose and into creative endeavour, emotional expression, etc. Pattern recognition, your example, can occur within more detailed mathematics in full relation to symbols on a paper alone, completely devoid of direct expressions in nature. These can be in the form of building blocks/proof steps, corollaries and the like towards larger proofs . . . the latter of which may or may not stand the scrutiny of time, even though they may or may not find representation in natural phenomena (as I mentioned above). We create constructs to fill in the gaps where observation fails and use them within the historically defined contexts of our mathematics language and its logical scaffolding to help increase our vocabulary and ability to make even abstract meanings sensible from a purely logic-based, abstractly provable perspective. It can be a focusing lens, sure. But, is all mathematics comparable to Newton's basic Laws, waiting for more granular and encompassing explanations of later derivations - such as from Einstein, et al - that mostly refine and define what is going on, chipping away at the unformed marble of our universal picture until it is fully revealed, ala Michelangelo? Eh, not all of it, but it seems our nature to attempt explaining things that we want to use for some purpose, eventually. The language and constructs in math didn't come about originally for nonsensible purposes, I suspect that it was originally all "applied" and only became theoretical as we began to create the constructs of mathematical language. Which then took on a life of its own, much as all languages are wont to do. Similar to how drawing helped to describe what we've seen, but eventually became recognized as valuable in even more abstract forms, revealing our emotions and indescribable ephemera as its application evolved among segments of the human population. Even today, we relate feelings, connect to situations or simply say much about nothing at all via verbal or written word - yet, verbal/written language can also be created and found valuable by and between humans simply as an abstract art, as well. Vaguely calling upon feelings, colours and realities, almost fully existing in concepts that never require constructs we can pin down and confine. It can become art, the domain of things we don't seek to explain but merely experience and appreciate. Or don't experience nor appreciate. That's art. Similarly, as expressed differently above, mathematics is more about art than description, I feel. It's taken remarkable imagination and creativity to derive the esoterica and even some proofs for fundamental concepts that we feel are rational and meaningful. Is it all stemming from an innate goal to (inadequately) describe the creation of what we perceive around us? Motivation is the key in your answer, I feel - it's somewhat obvious from where Plato was coming on that question. "So, please stay where you are. Don't move and don't panic. Don't take off your shoes! Jobs is on the way." [ Parent ] • ##### this is going to take more time...(0+ / 0-) ...to read and reply to than I have right now, because I have to scoot for a bit. I'll be back later today. Thanks -G2G • ##### We don't have to end up there(0+ / 0-) Mathematics is the language that we humans use to describe the world. It is not the language of God or of Nature. There are two options regarding the necessity of the truth of formal logic (and mathematics) 1. deny that they actually are necessary, and then account for why they only appear so, or 1. claim that the truths of logic and mathematics lack factual content - they are not "truths about the world" - and then explain how they are nevertheless true and informative. I choose the latter. Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?! [ Parent ] • ##### Plato was one nasty dude(1+ / 0-) Recommended by: wader Ever read the Republic? We all differ in ways that matter. But we're all the same in the ways that matter most. [ Parent ] • ##### I haven't eaten there yet, but (10+ / 0-) the pizzas sound good: π The crooks are leaving have left office, unprosecuted and scot-free fully funded, thanks SCOTUS. • ##### You know that left brain, right brain thing?(8+ / 0-) Whichever side does math, in my head, is retarded. Whichever side does language, in my head, is very smart, it seems to me. When subtracting my debits from my bank account, I sub-vocalize every step. "Seven minus eight is nine, and the six becomes a five...." So, even though I understand basically what pi is, I do not follow many of the other parts of this diary. I am interested in the debate about math being discovered or created by our brains. I have no ideas to add right now, but I find that debate easier to think about than actual complex math. Down to 6 billion by 2100. Got contraception? • ##### Seems to me an argument that(10+ / 0-) intelligence runs through existence. It runs through our inner and outer worlds as of a piece. So, we can say "well, 4,012 drops and the cup overflows" and at 4,012 drops the cup overflows. And this applies any other precise thing we can do with materials and vibrations (say, in music). At the same time, mathematics is a symbol-system for communication, and prone to the same advantages and defects of any other symbol-making process. So it might or might not have correspondence in any given case to what is actually occurring. Until we break the corporate virtual monopoly on what we hear and see, we keep losing, don't matter what we do. • ##### At first read, (5+ / 0-) and second read, that sounds right, but I cannot say exactly why. It just seems as if, it feels as if, that may be correct, what you wrote. Cuz symbols, parables, can be so very useful, then, at times, they can break down and not work. The Bible, by the way, I feel, is a collection of parables. Except Ecclesiastes, which is simple nihilism, which is true. Down to 6 billion by 2100. Got contraception? [ Parent ] • ##### Because someone has to say it...(13+ / 0-) Pi r not squared. Pi r round! Hoping and praying that the empty chairs and empty tables in Iran when all is said and done are as few as possible. • ##### So bye bye(9+ / 0-) Miss American Pi Watch this space. -5.13/-3.38 • ##### simple truth that 2+2=4(8+ / 0-) Is also true in number bases 5,..,\infty Copy editor by day; typo creator by night. • ##### Pi-yi-yi! n/t(5+ / 0-) "So if you don't have any teeth, so what? ... Isn't that why they make applesauce?" -- GOP leader Rush Limbaugh • ##### These Pi Day celebrations(13+ / 0-) are irrational exuberance! Obama: "I ask Congress to finish its work." Rep. Parker Griffith (R-AL): Health Care Bill "must be stopped". Which side are you on? • ##### A couple of thoughts(8+ / 0-) Some animals can apparently count. For instance if a small group of crow hunters (about 6 or fewer) enter a woodlot, then leave behind 1 member in order to set up an ambush for returning crows, the crows frequently will not return until the remaining hunter also leaves the woodlot. Use a group larger than about 6 and the birds begin to have difficulty understanding whether or not 1 person is missing from the party. "Invention" is a concept humans arrogate for themselves. Therefore, counting crows cannot invent. Since the crows have some understanding of math, math must be a discovery rather than an invention. Next thought: Taking pi to 4 decimals gives me a really accurate circumference for purposes of machining just about anything I'd want to machine. In practical terms, the remaining "infinity minus 4" digits to the right of the decimal aren't good for much. The Ancients muddled along just fine without them. • ##### My little dog(3+ / 0-) knows how to do peek-a-boo. If he sees a human or a cat or any animal he wants to contact, and we go behind a building, he wants to hurry to the other side of the building, to catch sight of the other animal again. I read that newborn humans do not have that understanding, but my little dog sure does. Down to 6 billion by 2100. Got contraception? [ Parent ] • ##### counting and math(3+ / 0-) crows can do more than this, like dropping the pebbles into the jug to raise the water level so the crow can drink the water. I am not sure this is the same thing as higher level math, but I do agree that mathematics is something that is true whether anyone knows about it or not. In physics they frequently find applications for new mathematical thinking that verify new physical principles, such as the origins of the universe, or sub-atomic particles. We discover the math, then we find physical events that parallel the math, then we understand the universe a bit better! It's been like that long before Newton, although he exemplifies the most elegant example of this with the Calculus - which was independently discovered by Liebnitz (we still use Liebnitz' notation today, although we credit Newton with the discovery. If mathematics was invented, could you patent it? it is a fascinating question. In a democracy, everyone is a politician. ~ Ehren Watada [ Parent ] • ##### Mind blown. Going to bed.(9+ / 0-) Getting up an hour early and having 3.14159265 for breakfast. respice adspice prospice • ##### Let them eat cake.(5+ / 0-) Well? Had to be said. Down to 6 billion by 2100. Got contraception? • ##### I'm pleasantly surprised to see that you...(6+ / 0-) didn't include a poll with you-know-what as an option. The man who moves a mountain begins by moving away small stones. -Confucius • ##### 14 -nt(1+ / 0-) Recommended by: sceptical observer • ##### Names(0+ / 0-) I cannot take anything seriously written by someone who has chosen to be publicly represented by the name "Rimjob." By knowing that the use of the term would offend some readers, you have apparently decided you don't care what those readers think. So why should they care what you think? • ##### A pi diary(4+ / 0-) and no poll with a "pie" option? That is a fundamental pun opportunity missed. "...but Scott Brown has a pickup truck."-my response to conservative rage • ##### Since one of my favorite subjects is Math(4+ / 0-) it's my obligation to wish everyone a happy Pi Day! Gee, I wish I had some pie right now! (*cue iconic comedy drum beat*) AHAHAHA...! ;) Socially liberal, environmentally conservative, economically centrist. • ##### In the Timex Sinclair 1000 home computer...(9+ / 0-) Shown here for$49.99 (!!!) in the states  and with a whopping 2K of internal memory (expandable to 16K--which is 0.016 megabytes of RAM):

Memory was very limited, so programmers had to use every trick they could to save memory.  One such trick was to use the PI constant instead of the required floating point number:

NOT PI = 0
SGN PI =1
INT PI = 3

Hey, don't laugh!  LET A = NOT PI saved 3 bytes!  When you only have a few thousand to work with, that means a lot!

That is my PI lesson for the day!

I still can't figure out how people actually "calculate" PI from scratch.  Maybe some mathematician can tell me.

DARTH SPECTER: I am altering the deal! Pray I don't alter it any further!
LANDO REID: This deal keeps getting worse all the time!

• ##### I so wanted one of these!(2+ / 0-)
Recommended by:
LordMike, rockhound

I dreamed of owning one of these Timex Sinclairs with the 16K expansion module. Instead, my first computer was a Coleco Adam.

• ##### You "dreamed" about gettinga sinclair computer?(0+ / 0-)

Believe me... they weren't that great.  The were a wonder of engineering in that they managed something workable with extremely limited and cheap hardware, but that was about it.

It had  no color... no sound... low res graphics.... the rampack would fall off the middle of typing... if you wanted any speed, you had to turn the screen off... modern TV's won't even accept the input 'cos the signal is so low.

Trust me... you were way better off with the Adam!

DARTH SPECTER: I am altering the deal! Pray I don't alter it any further!
LANDO REID: This deal keeps getting worse all the time!

[ Parent ]

• ##### Maybe(1+ / 0-)
Recommended by:
LordMike

But I really wanted to write killer programs like
10 print Hello;
20 goto 10

And I had to wait 2 to 3 years before I finally got the chance.

• ##### The Adam could do that....(0+ / 0-)

...and more!

DARTH SPECTER: I am altering the deal! Pray I don't alter it any further!
LANDO REID: This deal keeps getting worse all the time!

[ Parent ]

• ##### I had one of those!(1+ / 0-)
Recommended by:
LordMike

I used it as a doorstop.

• ##### if you divide 22 by 7(2+ / 0-)
Recommended by:
LordMike, carlos the jackal

you make a good start

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### The Leibniz formula!(1+ / 0-)
Recommended by:
LordMike

4 - 4/3 + 4/5 - 4/7 + 4/9 ....

(It's not fast, but it'll get you there!)

• ##### huh(4+ / 0-)

and just before this I was reading about a culture that has absolutely no concept of numbers.

http://www.spiegel.de/...

tunesmith's latest song: Damn My Eyes

• ##### Noam Chomsky was wrong(0+ / 0-)

Noam Chomsky claimed that no such language could exist. Yet it does. Further proof that he is full of shit.

Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?!

[ Parent ]

• ##### It was the hardest thing I had to learn to type(4+ / 0-)

from handwritten manuscripts, and I was secretary to, no I am not  going to say who, he is world famous, and his works will go on until the end time.   I am retired now from the UC system, and I will not disclose who I worked for.
Your diary just brought to light how difficult it was for me and the politics.  Let us have some 'pi' now.
Cheers.

• ##### Not as important as 42, of course(6+ / 0-)

But, yeah, okay. Pi is pretty important and interesting ;)

Seriously, as a scientist, I doff my chapeau at your awesome diary. Thanks.

Have a slice of ... oh, nevermind.

Become an Eclectablog fan on Facebook.

• ##### Thanks for remembering!(4+ / 0-)

After paying a lot of attention to it, Mr Mo (mathematician) and I actually forgot about it until this morning (though it was technically still Pi Day in California). We were distracted by voting in France and by Youngest leaving a Big Project to do until the very last moment.

Love me Pi, I do.

• ##### Discovery or invention.,,,(4+ / 0-)

it's still Pi. Mmmmmm,,,,,, Pi!

BORE, n. A person who talks when you wish him to listen. Ambrose Bierce, "The Devil's Dictionary"

• ##### I like pi(3+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority, UTvoter

Damn you and your faint praise!

• ##### Prof Steve Strogatz of the Nytimes had an article(3+ / 0-)
Recommended by:
TrueBlueMajority, UTvoter, angelajean

on imaginary numbers recently.

See here.

I don't understand the idea that imaginary numbers can't be ordered; the only metaphor I can make is trying to line up different fruit based on some abitrary concept of order.

• ##### Imaginary numbers CAN be ordered(1+ / 0-)
Recommended by:
TrueBlueMajority

Imaginary numbers are of the form 3i, -2.6i, 3.14159i, etc., where i squared is minus 1. They can be ordered in the same way as (real) numbers without the i.

You're thinking of complex numbers, which are represented as a sum -- one part of the sum is real and the other part is imaginary: 2.3 + 1.6i. There is no mathematically useful order for complex numbers. For example, which would be bigger: 3 + 5i or 2 + 6i? Neither choice advances any mathematical or physical ideas, and complex numbers are extremely useful in mathematics and in physics.

But just because there's no useful order for complex numbers doesn't mean that complex numbers can't be ordered. There are infinitely many possible orderings. One ordering would be: A + Bi is bigger than C + Di if A is bigger than C or if A equals C and B is bigger than D. (That's called a lexicographic ordering; it's similar to how we order words in a dictionary.)

If you don't know where you're going, any road will do.

[ Parent ]

• ##### one of the commentors in the strogatz (0+ / 0-)

i would think that by extension, complex numbers wouldn't be either.

• ##### Euler's number(7+ / 0-)

I'm glad you mentioned Euler's identity. While I think pi is very important, I believe that Euler's number e is the most important constant in Mathematics, and sadly gets short shrift in the layman's world view. e is the workhorse of Mathematics, and is stunningly poorly known.

Unfortunately, if we ever had an "e day", most people would probably be celebrating something else entirely, though it would be one heck of a rave. :-)

• ##### Mmmm....(4+ / 0-)

Kossack π....

This space available. Bad credit, no credit, no problem! Financing available!

• ##### Thank you for the informative Pi Day special.(5+ / 0-)

"Try not to become a man of success, but rather to become a man of value." ~ Albert Einstein

• ##### Yeah, but ...(1+ / 0-)
Recommended by:
UTvoter

... stop picking on the president.

• ##### Tipped, Recced for Pi! what, no poll :-) it was (5+ / 0-)

the perfect set up!  yay for math in the morning.

"For the cost of deploying one soldier for one year, it is possible to build about 20 schools." N. Kristof

• ##### Jeez, rimjob! You've done it NOW.(6+ / 0-)

.
Just wait til Beck sees that this diary tops (or comes near the top of) the Daily Kos Rec List.

He'll go ape on his Conspiracy Blackboard and demonstrate beyond doubt that  Daily Kos = Pi = Egyptians = Nasser = Soviet Influence = Obama = Profits . . . which you can't spell without "P" and "i" !!!

Won't somebody think about the hampsters???

.

"I have to go now. I feel . . . sticky." Anthony Bourdain

• ##### perhapos Beck will think it is an "n"(1+ / 0-)
Recommended by:
BenGoshi

and expect a diary about the n word

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### DKPENSOP?(0+ / 0-)

The thot plickens.

It's the economy, stupid!

[ Parent ]

• ##### great diary and thread, thanks! can you change(2+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority

font so that pi in title looks less like n? (n is still an attractive diary title - that's why I started reading, thought it was about n)

Viva Obama

• ##### i don't think you can format in diary titles(0+ / 0-)

you have to take what kos gives you

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### Then there is interestingly named PI(3+ / 0-)
Recommended by:

I can live with doubt and uncertainty and not knowing. I think it is much more interesting to live not knowing than to have answers that might be wrong- Feynman

• ##### a history of pi(3+ / 0-)

by Petr Beckmann, the book that taught me to love math.

• ##### This will be our math lesson at home today.(5+ / 0-)

It's why I love homeschooling. We can take advantageous of great resources when they appear.

Thanks for this great diary.

• ##### Did you see this(0+ / 0-)

from one of the links?

Pi Day at SBU

We homeschool, too. I think we're going to bake some pies today. I have different sized pans and we'll measure each and see how no matter the size, the ratio is constant. Fun! Yummy!

There's a reason Democrats won massively the last two cycles, and it wasn't because people were desperate for "bipartisanship". --kos

[ Parent ]

• ##### I missed this before I could rec(0+ / 0-)

Thanks for the link!

• ##### A quote from Bertrand Russell(5+ / 0-)

who not only knew his math, but was one of the few people to protest against both WW I and Vietnam.

Mathematics is the only subject in which we never know what we are talking about nor whether what we are saying is true.

We all differ in ways that matter. But we're all the same in the ways that matter most.

• ##### 1 + 1 = 2 is a VERY difficult notion(6+ / 0-)

In Principia Mathematica, by Russell and Whitehead, it takes several hundred very VERY dense pages for them to prove it is so

We all differ in ways that matter. But we're all the same in the ways that matter most.

• ##### It's difficult for conservatives, too(1+ / 0-)
Recommended by:
plf515

They're all pretty convinced that 1+1=3, enough so that they're willing to ban abortion and contraception.

• ##### What a deee-lightful diary!(2+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority

Thank you!!

Medicare for All is a shovel-ready project!

• ##### What is randomness?(5+ / 0-)

Proving that pi is random is tricky, partly because of the nature of pi, but in large part because we don't really know precisely what 'random' means.

Tests of random number generators get more and more complicated.

You might think that not being able to predict the next digiti in a number means the number is random.  But not so.  Take the digits from 0 to 9.  Put them in a hat.  Now, mix them.  Then pull them out.  Write them down in the order you pulled them out, getting something like

147852369

do it again, add that

1470852369785409631

and so on.

Now, every set of ten digits in that number has all the digits 0 to 9, so the whole thing is not really random, but you can't predict the next digit.

We all differ in ways that matter. But we're all the same in the ways that matter most.

• ##### What does Pi look like in other number systems(3+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority, Catte Nappe

Such as binary or hexadecimal?

I don't really understand the advanced math stuff, but might Pi repeat if looked at using a different number system?

"Suviving a Traumatic Brain Injury: A Family Guide" is now available online: http://www.braininjurysuccess.org/

• ##### No(5+ / 0-)

A number that repeats in any base is a rational number. Rationality is a concept that does not depend on base but rather on the fact that a rational number is the quotient of two integers, and integers are integers regardless of base. Pi is not rational, so pi does not repeat in any base.

If you don't know where you're going, any road will do.

[ Parent ]

• ##### now THAT is the coolest thing i ever read(2+ / 0-)
Recommended by:
Catte Nappe, carlos the jackal

Pi is not rational, so pi does not repeat in any base.

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### Pi =1(1+ / 0-)
Recommended by:
sargoth

in base Pi

"The authorities aren't interested in the truth, merely in authority."

[ Parent ]

• ##### A transcendental diary!(3+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority, indybend
• ##### All I know...(7+ / 0-)

...is that in order to calculate the area of a tire contact patch so that cargo aircraft floor limitations aren't exceeded is to measure the length and width of the actual contact patch (stick a piece of paper under the front and rear for the length, under each side for the width) then multiply these values, then multiply the result by . 785 for the area of the patch....Did this for years without giving it any thought, then one day an Instructor pointed out that .785 = 1/4 Pi (cue harp flourish here...)

Arguably, this is an approximation, the patch is probably actually an oval, but the recognition of using 1/4 Pi to extract the parts of the square not contacted by the tire led to some inkling of the oddity inherent in Pi...

(using this method, you'll find that a 200 lb man on a road bike with 23mm tires can't ride inside the cargo compartment in flight without exceeding the floor limitations of certain cargo planes, the resultant area is less than 1 square inch per tire, so the result is over 100 psi and we had a flight limit of 50 psi for the floor-this calculation is the result of having too much time on our hands on long over-water legs...)

(Hey, some people post pix of cats, others post recipes, I'm telling how to calculate a floor limit for an aircraft that doesn't even exist any more...)

"Ronald Reagan is DEAD! His policies live on but we're doing something about THAT!"

• ##### It's a floor wax AND a dessert topping!(4+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority, rockhound, JeffW

It's a discovery AND an invention!

Now people can argue about which came first. :)

"A riot is an ugly thing . . . and I think it is just about time we had one!" -- Inspector Kemp, Young Frankenstein

• ##### Thanks for the great piece! My two cents...(4+ / 0-)

While the shape and pronunciation of numbers are human constructs, things exist, and they exist in quantities. The relationships of these quantities seems to amount to math in practice, and any beings capable of analysis will discover the relationships of the quantities of things.

You're welcome. lol

"The only maxim of a free government ought to be to trust no living man with power to endanger the public liberty." - John Adams

• ##### i wish i could recollect pi easily today(4+ / 0-)

Can a mathematical truth really exist before anyone has ever imagined it?

of course!  and pi is a perfect example of that!

the circumference to diameter ratio of a circle existed before human beings were rolling logs to make wheels.  coming up with something to call this beautiful phenomenon is a human invention, but the ratio itself was not invented by humans!  :-D

bonus points to the first person who gets the reason for my subject line...

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

• ##### Hmm. I know a sound reasoning is hidden there(1+ / 0-)
Recommended by:
TrueBlueMajority

"A *person* is smart. People are dumb, panicky, dangerous animals and you know it. " Kay (Men In Black)

[ Parent ]

• ##### COOL! I never heard that one before!!! n/t(0+ / 0-)

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### Sorry,(1+ / 0-)
Recommended by:
TrueBlueMajority

Didn't know it was supposed to be pre-existent. I made it up.

Unlike Pi, and mathematics, in general, which is a discovery.

"A *person* is smart. People are dumb, panicky, dangerous animals and you know it. " Kay (Men In Black)

[ Parent ]

• ##### even cooler...! n/t(0+ / 0-)

"Politics is like driving. To go backward put it in R. To go forward put it in D."
--Tom Harkin

[ Parent ]

• ##### Ratio is a human construct(0+ / 0-)

Just like circumference and diameter. They are descriptions of the world an not things-in-themselves.

Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?!

[ Parent ]

• ##### Frank Booth in misunderstood(0+ / 0-)

Dorothy was the one who was really in charge. Slaves always are.

Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?!

[ Parent ]

• ##### Pie!(2+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority
• ##### Hell, a vote against war = a vote against...(0+ / 0-)

...hatecrime legislation if the party demands it.

everything is applied mathematics
the rest is pure mathematics

[ Parent ]

• ##### It led me down a bad path.(2+ / 0-)
Recommended by:
Rimjob, TrueBlueMajority

We had to have pie for dessert, just to celebrate. It was key lime.

Now Pi Day is over, but I still have 3/4 of a key lime pie in my fridge.

The only thing we have to fear is fear itself.

• ##### Showing Kids Pi(9+ / 0-)

This isn't a post with high-order mathematical thought - only something I used to do with school kids.

I'd bring in some canned goods - and try to get 6-10 different sized cans. I'd also bring in string (or masking tape) and yardsticks.

Students, working in groups, would do their best to measure the distance across the top of the cans. Then they'd wrap the string around the can (or the masking tape), mark the start and end point, and measure the length of the string or tape. Lastly, they'd divide the length of the string or tape by the length of the distance across the can.

The answers would vary, of course, but then I would ask what might happen if we had the best measuring tools in the world. Invariably, someone would say, "We'd all get the same answer."

Bingo! Now you could tell them about pi.

I am retired now, but teaching high school math to aboriginal adults. I tried this again last week and it still works like a charm.

Canada - where a pack of smokes is ten bucks and a heart transplant is free.

• ##### I teach math teachers(2+ / 0-)
Recommended by:
dpc, ImpeachKingBushII

and I always point out this activity to them.   Most of them did not do it in middle or elementary school, but I think they will as teachers.  A slight variation is to do lots of measurements and average the results for a better estimate.   Hula hoops are good too!

• ##### Throwing frankfurters at a grid of equally spaced(0+ / 0-)

lines is a great way to get kids to "find" pi.

"The authorities aren't interested in the truth, merely in authority."

[ Parent ]

• ##### Frankfurters?(0+ / 0-)

"The authorities aren't interested in the truth, merely in authority."

[ Parent ]

• ##### What!?! No Poll with "π" as the only answer?(2+ / 0-)
Recommended by:
Rimjob, ImpeachKingBushII

Interesting stuff. I got to Calculus III in college and never actually understood this about Pi.

Call it the 'Corporate New Deal' or a 'Plastic Democrazy'© if that makes you feel good. I call it Fascism.

• ##### What do you get if ...(2+ / 0-)
Recommended by:
Rimjob, kev9100

..you divide the circumference of a turkey by it's diameter?

Turkey Pi !!!!

• ##### e i n stein/happy birthday(2+ / 0-)
Recommended by:
Rimjob, carlos the jackal

as explained by the diarist:
e, i, n, + stein (german for stone, expressly a stone or boundary marker, or one who lived near a castle or the boundary)

Happy Birthday, Albert.  We miss you.

If the only tool you have is a hammer, every problem looks like a nail.

• ##### Can we have a moment of silence and a disintegrat(1+ / 0-)
Recommended by:
carlos the jackal

ing cassette tape for Peter Graves in honor of his life?

This is the most Killer rendition of Mission Impossible that I have heard. Thanks Laika and the Cosmonauts

Slow thinkers - keep right

• ##### Awesome accompaniment(0+ / 0-)

to the animation in diarists tip jar!

There's a reason Democrats won massively the last two cycles, and it wasn't because people were desperate for "bipartisanship". --kos

[ Parent ]

• ##### Discover/invent(1+ / 0-)
Recommended by:
Rimjob

It doesn’t require a God in any traditional sense, but it does require "structures of pure idea and pure being," he says. Defending such a position requires "abandoning the arsenal of rationality and relying on the resources of the prophets."

Personally, I bow down and pray 5 times a day to the number 9.

But, if mathematics were invented by us and not discovered, would the other spots in the Universe we observe be obeying different laws? Our calculations for them would be incorrect?

"If religion is the opiate of the masses, then fundamentalism is the amphetamine." Miz Vittitow

• ##### Nothing to say but that I loved this diary(1+ / 0-)
Recommended by:
Rimjob

and wish I had a lot more time to spend on it.  Musings like this can change the world in a way politics never can.

Perhaps everything terrible is, in its deepest being, something helpless than wants help from us.

• ##### Math is discovered!(4+ / 0-)

I analyze thus:

It is possible that the universe is merely an illusion, as am I. In which case mathematics is just one of the illusions. In which case I am free to treat it as being as real as anything else. So it works out the same as if the universe is real.

Treating the universe as real:

1. The anthropomorphic principle states that we cannot deduce the existence of a Creator from the fact that the universe supports human life. Since we are here to observe the universe, the rules by which the universe operates must be amenable to our sort of life. We are here, so we are here.
1. If the universe is not orderly, and the rules can change arbitrarily, than this implies that life cannot have evolved over billions of years, and also that there is an external force which acts upon the universe to change the rules, and which created us. This implies a chaotic, capricious Creator. Referring back to rule (1), we can neither prove or disprove the existence of such a Creator.
1. Assuming that God != chaos, the existence of orderly rules means that there must be a language in which those rules can be written down. From a purely software viewpoint, if you can't express the algorithm in any language, then the algorithm doesn't exist. Mathematics is the language in which the rules of the universe are written, and therefore mathematics exists independent of the universe!

I conclude, therefore, that either there is a capricious, chaotic Creator mucking about with our minds, or mathematics is a beautiful language in which a possible-but-not-necessary Creator writes the rules of the universe.

Your mileage may differ.

In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra

• ##### I deny that it is possible that (2+ / 0-)
Recommended by:
ImpeachKingBushII, SoCaliana

the universe is merely an illusion.  That would make you an illusion too, you know, because you are part of the universe.

Our thoughts are themselves facts as well.  And all facts are constituents of the universe.

The usual way of treating the natural world as an illusion maintains the existence of the stream of thoughts (the subject of the illusion) outside of time and space and nature.  It then contends that this stream could be creating the impression of a natural world, like we experience in a dream.

But the stream of thoughts is itself part of nature, and so must be creating an illusion of itself if nature is an illusion.

This however is impossible.

Youth lives by personality, age lives by calculation. -- Aristotle

[ Parent ]

• ##### And I assert(0+ / 0-)

that a difference which makes no difference is no difference. If it is not possible for me, inside the illusion, to discern the illusion, then for me it is not an illusion. So for practical purposes the illusionary universe may be ignored.

In theory, there is no difference between theory and practice; but in practice, there always is a difference. - Yogi Berra

[ Parent ]

• ##### Solipsism is like crack for some people(0+ / 0-)

Just say no.

Shut up! It's Daddy﻿ you shit-head. Where's my bourbon?!

[ Parent ]

• ##### I realized late last night(8+ / 0-)

that I had missed Pi Day, but since I'm in Indiana, I've decided to round up to March 15th and celebrate anyway. You can do that sort of thing in Indiana.

Great diary!

There's a reason Democrats won massively the last two cycles, and it wasn't because people were desperate for "bipartisanship". --kos

• ##### Elect more mathematicians to the legislature!(4+ / 0-)

The Indiana Pi Bill is the popular name for bill #246 of the 1897 sitting of the Indiana General Assembly, one of the most famous attempts to establish scientific truth by legislative fiat. Despite that name, the main result claimed by the bill is a method to square the circle, rather than to establish a certain value for π, although the bill does contain text that appears to dictate various incorrect values of π, such as 3.2.
The bill never became law, due to the intervention of a mathematics professor who happened to be present in the legislature.

Indiana Pi Bill

• ##### n times zero is so Republican (7+ / 0-)

N*0 = 0

If cats could blog.... they wouldn't.

• ##### Like the picture in the (1+ / 0-)
Recommended by:

first block quote.

I'm HOT for teacher!

"Wide acceptance of an idea is not proof of its validity." Dan Brown

• ##### For Physics to Hold Throughout(4+ / 0-)
the Universe, how could man have invented mathematics as in, created it from nothing, like language.

Man invented numbers and the application of mathematics which is, in part, a means of expressing numerical relationships and physical laws that he didn't invent, but that appear (by observation and experiment) to hold true throughout the Universe.

A nice discovery to learn that math works.

"ingratiation and access . . . are not corruption." -- Justice Kennedy (Citizens United v. Federal Election Commission, 2010)

• ##### Constant?(4+ / 0-)

I think the value of pi varies with the curvature of space.

• ##### I tried that one on an exam...(1+ / 0-)
Recommended by:
blueyedace2

no dice!

"Who is John Galt?" A two dimensional character in a third rate novel written by Alan Greenspan's dominatrix.

[ Parent ]

• ##### What about "e"?(5+ / 0-)

Most of my serious quantitative skills from engineering school have fallen out of my brain.  But "e" seemed to show up just about everywhere in that minimal number of electrical engineering and physics courses that I was able to survive on my way to a computer science degree.

• ##### Sweaty palms, rapid heartbeat(4+ / 0-)

Your diary brings back the old, familiar panic for those of us who struggled with math. An algebraic equation can still throw me into a panic attack; physics can still bring me to tears. I can diagram any sentence, learn languages and deliver an extemporaneous speech to a crowd of any size, but still have limited mathematics skills.

I'm proud to say that I was able to gain a basic understand of pi and have nothing but the greatest respect and admiration for mathematicians.  Somebody has to do it.

"Private health insurers always manage to stay one step ahead of the sheriff." Sen. Sherrod Brown

• ##### right there with ya(2+ / 0-)
Recommended by:
blueyedace2, Betty Pinson

Putting on the spectacles of science in expectation of finding an answer to everything looked at signifies inner blindness. -- J(ames) Frank Dobie

[ Parent ]

• ##### massive tired head(3+ / 0-)

I am certainly glad that there are math humans out there because if it was left up to me we would still be using beans and small stones to count.

I cannot find proper words to express the feeling of joy that I experienced the day I knew that I had fulfilled the required portion of calculus and I NEVER HAD TO TAKE IT AGAIN!

Putting on the spectacles of science in expectation of finding an answer to everything looked at signifies inner blindness. -- J(ames) Frank Dobie

• ##### Definition of a mathematician: Someone who thinks(4+ / 0-)

that the Tennessee Titans used to be the Houston Eulers.

• ##### mahalo (2+ / 0-)
Recommended by:
Rimjob, blueyedace2

I'd forgotten the joy of learning, especially mathematics which is a poetry of sorts. Thanks.

• ##### Mathmatics evolved(0+ / 0-)

Sir Isaac Newton is my second cousin, nine times removed. Really. Maybe my interest in science and mathmatics evolved from a few of his genes. Nah, I just like pie.

Insert your circular argument [here...]

I know you believe you think you understand what you thought I said, but I'm not sure that what your heard is exactly what I meant.

"I believe in eight of the Ten Commandments" - Steve Martin

• ##### My distant ancestor was his tutor.(0+ / 0-)

I'll always credit my family tree for Newton's ability to express his genius.

Not really, but it's kind of a cool connection though.

• ##### Sarah Palin is my 9th cousin - 'nuff said n/t(1+ / 0-)
Recommended by:
Indexer

"I believe in eight of the Ten Commandments" - Steve Martin

[ Parent ]

• ##### I got to wear my Pi day pin at school on Friday.(1+ / 0-)
Recommended by:
IL JimP

The kids all thought we were super nerds. On the plus side the boss brought in lots of pies. Being a teacher is awesome sometimes (okay well most of the time).

"indifference is the one thing that makes the very angels weep."-Cornel West

• ##### Numbers are like knowledge...(0+ / 0-)

...philosophically speaking, they are intertwined and meshed together forever and inseparately, whether anyone is around to witness it or not.

We don't know all there I to know, sometimes even when the truth is standing there right before us. The universe is composed of known knowns, known unknowns, unknown knowns, and unknown unknowns. Words, too are like numbers. They can be configured into equations, in constants and variables. I see the universe as a composit or dumping place for both numbers and knowledge, unlimited and breadth and depth. The denser the brightest stars among us, the more numbers and knowledge gravitates to these. The lesser the density the less the intensity. Einstein said that we use only about 3% of our working brains, but this doesn't limit the vast potential for greatness or excellence that each individual has within their own grasp. We are only limited by the prisons we have made within our own realms(minds). A prism divides the light into 7 distinct basic colors, but coming together we see what we call light! Divided each color is limited, but in coming together as one, we find the potential --just like pi-- to be virtually and forever unlimited! Look at the speed at which light travels! Einstein sat for hours and calculated and with his General Theory of Relativity, he hit upon the truth of the ages! Light bends without breaking! And so it is the natural progression of things, so it is with the truth!

"Peace is the protector of genius. War is the mortal enemy of both peace and genius."

• ##### Where-oh-where is the Pi poll? n/t(0+ / 0-)

I refuse to accept "no can do" as a proper slogan for progressives.

• ##### I vote for "Both"(1+ / 0-)
Recommended by:
Rimjob

The quintessential philosophy that embraces the "Both" approach is Buddhism:  The Buddhist concept of the "Three Aspects" posits that reality is not just existence versus non-existence. Instead, all phenomenon are seen an inseparable combinations of  Appearance, Nature, and Essence.

Water has an appearance (matter) we can measure (clear, liquid, one kilogram/liter weight, etc) and a nature (spirit) that we cannot (life-sustaining, cleansing, etc.)  Just because Hydrogen and Oxygen have not yet combined would you say that water doesn't  "exist"?  Water's potentiality is in a state of "Ku" or potentiality.  The essential identity of water is neither its appearance or nature, but the integration of both. Essential identity transcends the existence vs. non-existence dichotomy and thus transcends time and space as well. However, essential identity is what supports and integrates appearance and nature simultaneously in the subject-object universe our minds perceive.

Both Deists (Hindu, Jew, Christian, Muslim, etc.) and non-deist (Buddhist, Taoist, Atheists, Rational Materialists, etc.) can imagine that the universe and all its potentialities are eternal. Other big bangs might happen outside the universe we can measure, and if a creator god is eternal then its  eternal creative nature must express itself again after the destruction of the universe we can measure.

From the standpoint of the "Three Aspects" Man and Math have both eternally existed. Therefore, Math is BOTH an invention and a discovery.

I'm already against the next war!

• ##### PHI(1+ / 0-)
Recommended by:
Rimjob

PLEASE donate to a global children's PEACE project: Chalk 4 Peace

• ##### We discovered the math that is constant in (1+ / 0-)
Recommended by:
Rimjob

the universe- we just gave it a language and names so we can use it to interpet the universe.

IMO.

• ##### great geeky diary.(1+ / 0-)
Recommended by:
Rimjob

lots of worthwhile interesting comments.

where's the picture of Bluto wearing the 'COLLEGE' sweatshirt?   need that.

piece

"Sell 'crazy' someplace else, we're all stocked up here." -Melvin Udall