1
$\begingroup$

A mad scientists constructs a device which changes Pi instantly from 3.1415... to something like 4.7182...; it is still an irrational number but it is different.

What changes would happen?

The things that I have thought of already are:

  • Earth gets a different circumference and volume, meaning an increase in mass and higher gravity.

  • Cars and bicycles become faster because while wheels rotate at the same speed, they cover a larger distance.

  • Atom structures are changed due to a change in the orbits of electrons.

  • The orbit of the earth gets longer, meaning a longer year. However, because the Sun's mass is increased, the gravity is increased, meaning that the earth's orbital speed increases.

Or will the entire universe just break?

$\endgroup$

closed as too broad by Xandar The Zenon, Neil Slater, Hohmannfan, overactor, Frostfyre Feb 28 '16 at 16:20

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

  • 3
    $\begingroup$ Increasing the value of pi would mean you'd increase the curvature of the universe. But I can be wrong. $\endgroup$ – CerebralFart Feb 28 '16 at 14:39
  • 1
    $\begingroup$ You've changed my world in an inconceivable way, a way in which we have no idea the reprecussions, or how it will work. So I think this is too broad. $\endgroup$ – Xandar The Zenon Feb 28 '16 at 14:59
  • $\begingroup$ See the works of Bergholt Stuttley "Bloody Stupid" Johnson for reference material on this problem $\endgroup$ – Separatrix Feb 28 '16 at 15:08
  • $\begingroup$ I think math.stackexchange.com/questions/53023/… answers your question. $\endgroup$ – Xandar The Zenon Feb 28 '16 at 15:28
  • 3
    $\begingroup$ The value of $\pi$ is just an observation. This is a bit like asking "what if the sky was green?". Well, it could be -- especially if you define "green" to be approximately 450 nm. If you want a world in which the ratio between an ideal circle's radius and its circumference is something like 4.7182 instead of something like 3.1516, you should decide what could cause such a change, and investigate the effects of that change. My guess, like James Kilfiger, is that you'd effectively break the universe. $\endgroup$ – a CVn Feb 28 '16 at 16:31
8
$\begingroup$

You first have to decide what you mean by pi. You can define it by, for example the limit of the series $$\pi=4\sum_0^\infty \frac{(-1)^n}{2n+1}$$, in which case it's value is fixed by the axioms of the real numbers. You can't get a different value without changing what you mean by "number". Which means that you haven't really changed it, you have just started talking about something else....

You can the classic definition of the ratio of the circumference to the diameter of a circle. And here there is a bit of wiggle, because in curved, hyperbolic space, the value of pi would be dependent on the size of the circle, with larger circles having a larger value for this ratio. Usually instead of saying that pi changes, we just say that ratio changes, and it does so according to the formula $$\mathrm{``Hyperbolic\ \pi"} = \frac{2\pi\sinh(\mathrm{radius})} {\mathrm{radius}}.$$ In this world, pi is not a constant.

In this world space has a quite dramatic negative curvature. The relativistic implications of this are probably that everything collapses into a black hole. So I think we just broke the universe.

Perhaps you can see the diffculty if you consider "What if the number 7 changes to 9" well now it is not 7 anymore, it is 9!

If pi changes to 4.7182, it is not pi any more.

$\endgroup$
  • $\begingroup$ Given that the question makes no sense (not many WB questions do), even then this answer does not actually address the question. This makes it more of a glorified content than anything else. I suggest you go on to discuss the question in an edit, otherwise you might risk NAA flags. $\endgroup$ – Tamoghna Chowdhury Feb 28 '16 at 15:33
  • $\begingroup$ Also, to change pi, you could change the constant term 4 in the infinite series. $\endgroup$ – Tamoghna Chowdhury Feb 28 '16 at 15:34
  • $\begingroup$ You can actually accomplish this using only special relativity (in one dimension anyways). If you spin a disk, the measuring rods on the circumference become shorter, but the ones on diameter don't. That means that if you are on the disk (which means for you, the measuring rods are length), the circumference will be more than π times the diameter. (Also, if the disk started at rest and is physical, it will probably break, because like the measuring rods, its circumference will also contract. en.wikipedia.org/wiki/Ehrenfest_paradox) $\endgroup$ – PyRulez May 9 '16 at 13:04
3
$\begingroup$

If you changed Pi, the only thing that would happen is that you'd irritatate everybody doing geometrical calculations because their nice easy C=2*pi*r equation becomes an ugly C=2*3.1415...*r Until they decide on a new symbol to use.

But if somehow you did "change the universe" then hopefully a plane would stop flying (because it relies on Pi), crashes into the scientist who ruined Pi and undoes the damage.

But really what you're asking cannot be done - it is a concept that does not make sense and really has no physical analog.

$\endgroup$
  • $\begingroup$ +1 It is akin to making blue color red. Or adding 90 more degrees of angle to a straight angle. Or staring yourself in the eye without the help of a mirror or reflecting surface ... $\endgroup$ – Youstay Igo Feb 28 '16 at 20:05
1
$\begingroup$

It isn't really possible to change the value of an actual number because the value of pi isn't really arbitrary. While it's possible to imagine a universe in which the laws of physics are different such as one where the speed of light is infinity or where there are four spatial dimensions it isn't really meaningful to ask about changing the values of numbers.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.