# Questions about phi and infinity?

Guys

How do you think our reality would differ if the phi ratio were exactly 3 ?

Is infinity a possibility? To me It must be, but in he same breath it cant be!!

"It is impossible to imagine an impossibility"

By the way I am a retired Mechanical Engineer (Electricity power supply)

Alan

I meant pi not phi??

Guys

How do you think our reality would differ if the phi ratio were exactly 3 ? (I meant pi of course not phi, but maybe this could be also part of this thread

Is infinity a possibility? To me It must be, but in he same breath it cant be!!

"It is impossible to imagine an impossibility"

By the way I am a retired Mechanical Engineer (Electricity power supply)

Alan

Alan

tiny-tim
Homework Helper
Hi Alan!
How would our reality would differ if π were exactly 3 ?​

π isn't part of reality … it's part of mathematics, and it can't be changed.

Were you thinking of any particular application for π?

tiny-tim,

However, pi is not just a mathematical truth as an Engineer I come across this daily. To drill a flange with six holes. The radius as you well know is always a little longer than six times the circumference. It would be nice if the great mathematical had thought of this dilemma for us Engineers, if pi were exactly 3 we could just take the radius and mark off exactly our 6 holes, and drill immediately. With millions and millions of said drilling happening every second, it would save an enormous effort and cost. The only way to drill 6 holes is to take the radius and adjust your protractor to a little less than the radius and by a process and get closer and closer until one gets to an exact division of 6.

On very large diameter flanges this becomes more and more difficult and more difficult for 12, 24, 36 holes etc etc.

Maybe in another reality or hypothetical universe the fabric of space would be slightly looser allowing pi to become exactly 3.

Of course you mathematicians might say this is just "pi in the ski" nonsense but it is nice to think of what we consider an impossibility

“It is impossible to imagine impossibility”

Regards

Alan

HallsofIvy
Homework Helper
Guys

How do you think our reality would differ if the phi ratio were exactly 3 ?
As other's have said, using mathematics in "reality" involves fitting the mathematics to the application. If "the phi ration" were some other number, we wouldn't use it in those same calculations.

Is infinity a possibility? To me It must be, but in he same breath it cant be!!
Define your terms. What do you mean by "infinity"? (I can think of several, very different, definitions in mathematics.) What do you mean by "a possibility"?

"It is impossible to imagine an impossibility"
And exactly what do you mean by that?

By the way I am a retired Mechanical Engineer (Electricity power supply)

Alan
Can you do anything about my high electric bill?

On a curving surface, you could define the distance between 2 points as the length of the shortest path between the 2 points on the surface. eg: when you fly from LA to NYC, the shortest path that the plane takes is actually a curving geodesic.

If you then define a "circle" to be the collection of points a fixed "distance" (the "radius") away from a point on the surface, then the ratio of the circumference to the radius will differ from 2*pi, and you would get a new value of "pi". A great circle on the unit sphere, for example, would have circumference 2 pi and "radius" pi/2 (remember, this is the geodesic radius on the surface). Thus circumference = 4 * "radius" = 2*"diameter".

Taking the example further, the value of "pi" on the sphere would depend on the radius of the circle in question! "Pi" is 2 for the great circle, and approaches 3.14... as the radius gets smaller and smaller since locally the sphere looks flat. Now, I can't really visualize it, but you could probably cook up a mathematical manifold (generalization of a surface) where the ratio of circumference to diameter of a circle on the manifold is 3 everywhere. The manifold would have to be curving inward everywhere in some strange way

tiny-tim
Homework Helper
Hi Alan!

If you mean could the ratio of the circumference of a circle to its diameter be different from π, the answer is that for very small circles it can't be, but for large ones (like a circle of latitude on the earth's surface) it can be.

Maze thank you ! good response

you said

Now, I can't really visualize it, but you could probably cook up a mathematical manifold (generalization of a surface) where the ratio of circumference to diameter of a circle on the manifold is 3 everywhere. The manifold would have to be curving inward everywhere in some strange way

Just because you cant visualise it does not make it impossible, but you said "cant really" so you came close

Hallso,

My point is that if pi of a circle "was" exactly 3 our reality would have to differ. Of course I "know" that it is 3.14........................................? In another universe why could it not be 3?

Infinity??

I know an unimaginably huge thing like the universe if for all intence and purposes to us puny entities it is infinite, "But it might not be infinite in truth".

What I meant about infinity , is imagine you where trapped, somehow, on a road that had no end or beginning, just extending in both backward and forward directions infinitely. How would you rationalise this subjective impossibility?

"It is impossible to imagine an impossibilty'

Imagine an impossibilty and we can dialogue futher

Alan

Well if what you're basically saying is if you went through every place in modern mathematics where pi occurs and just replaced it with 3 (and did so for all future times it may occur) then I don't see how it would change anything. We have no way of visualizing how a circle could obey the various properties of a circle and have pi=3 but if it somehow made sense then I suppose thing like exp(-i*pi)=-1 would still make sense and such but of course that universe could never exist (I don't think). The thing is Pi is not a physical constant it's a mathematical one, it can be precisely defined by an infinite mathematical series without any reference to things in the real world (like measuring the circumference of a real-world circle). You may have heard musings by physicists and such about how the universe would be different if the physical constants were different but they're not talking about Pi. They're talking about things like the charge on an electron and the fine structure constants which are EXPERIMENTALLY determined constants that have seemingly arbitary values. Once again, this is not $$\pi$$ which is precisely defined by a mathematical relation (for example if one expands 4*arctan(1) in a taylore series one will get Pi to as many digits as they desire they don't need to in any way interact with the real worl).