This was a thought that actually occured to me a few years back and Iâm glad Iâm not alone in the thought. My final conclusion then was that even though nothing in nature really seems to have infinite zeros after the decimal point, if we could instead measure the smallest particles (my assumption was electrons/protons/neutrons or maybe even quarks) we would have a rational number since thereâs only a finite number of particles. So our measurements would be precise to the point and rational. Does this seem logical?
And to back up anthem here, math is a concept irrelevant to time so stopping time would have nothing to do with it as infinite, or finite for that matter, has no âspeed(units/time)â, which seems to be your assumption superculture.
Thanks Rouz 
Yes it does, but I think the number of particles falls into the âhow manyâ camp as opposed to the âhow muchâ camp. When it really comes down to it, I think the âhow muchâ camp can be reduced to only continuous quantities such as space and time (in other words, not discrete âthingsâ that exist).
What youâve said still doesnât deal with my point: In the real world these numbers would go on forever, and they would have to be made of stuff, if you were to expand an infinite series, it would take up all matter in the universe pretty quickly, and youâd run out of stuff to make the next number in the series. i.e. they are numbers and functions, you have to get used to the idea that numbers are self-recursive functions, and when time stops these functions also stop
If the ratio 1/3 is a function, then itâs opposite 3/1 is a function and since even âirrationalâ numbers have a base, that means they must by definition be numbers and functions, for math to remain consistent, remember all numbers are made of the first, that is, 1. Therefore:
Pi is actually Pi / 1 (which is a function), you can only see it by representing numbers in total expanded form using shapes, and âstuffâ to make numbers out of. Numbers are not made out of non-existence, they are made of stuff that exists.
What youâve said is pure bullshit, numbers are functions, and functions only function if there is time, numbers are not made of non-existent stuff, I want you to grab apiece of paper and cut it into equal pieces and for each element of a number (say, 2 there is 2 squares, 3 there is 3 squares and so on), soon enough youâll run out of stuff to make numbers out of, your fallacy is that you think numbers are made out of non-existent stuff, that is why you canât grasp what I am saying and it is not an assumption it is a fact, you canât get a non-existent number from non-existence, period.
There needs to be a distinction between counting and measuring. You can count the number of atoms along the length of a piece of wood, and get a rational number, but how long is each atom? You end up with the same problem. And as we deconstruct particles further we find that the smallest parts may not even really exist at all times ( 
quantum physics is crazy). Itâs murky ground still, but the point is we canât get exact measurements because we still donât understand what goes on at the smallest levels
Ok, are you saying that you need to time to count digits, so that if time were stopped there would be no time to count digits and therefore the digit after you no longer can count no longer exist? That makes no sense to me. And why insist that numbers are made of physical stuff? Counting, and assigning numbers to things is a human concept. The fact that we use base 10 to count, or bases 2 and 16 in computers is an arbitrary human decision. Numbers, counting, units of measurement - all are human concepts that we use to describe what we see. Numbers donât have to exist in nature, only in our heads, and if thatâs the case, then there is no reason to limit them
Always good to see the products of an engineerâs mind 
Are you still a student by the way or postgrad, what are you studying?
Yup yup but a great many of these particles are naturally restricted to bigger particles and the smallest particles only exist at very small fractions of time and not in all conditions so it would be possible to get matter to a point where these particles wonât be emitted randomly, as far as Iâm aware. Measuring them in a hypothetical scenario still makes sense, we just donât have any equipment to measure something to that smallest possible point. Iâm assuming there is a smallest fraction. Perhaps something like an Avogadroâs number for length? My assumption is that since everything is finite from base to whole, if we were to make an infinitely accurate measuring device, weâd end up with a rational number.
I used to think of the possibility of âsmallest possible movementâ by any particle which would imply that a particle can only move 0.00âŚ1m at a given time and not 0.00âŚ05m to rationalize movement as finite as opposed to infinitely small. Possible?
If self-righteousness and emotionally triggered insults were indicators of being correct, youâd be have the final say. Numbers are concepts. Youâve said âif you were to expand an infinite series, it would take up all matter in the universe pretty quicklyâ. Weâre saying it doesnât do it âpretty quicklyâ, it doesnât have time. Two infinites donât reach a given number at different times, infinite doesnât work with speed, it isnât a number, itâs a concept and itâs irrelevant to time. Freezing time doesnât let you count [x/0] or pi, assuming you werenât frozen. Pi will be irrational at 0 time or at infinite time.
Youâre assuming that things are constantly growing in time as one goes to smaller measurements. I assure you they arenât. You can measure the weight of something (and weight measurements are quite accurate), and then measure its length to the smallest possible accuracy. Its weight wonât change regardless of how small you go. Freezing time is irrelevant.
Saying something is bullshit just shows that it opposes your views and that youâre disrespecting the person due to an inability to present a viable argument. If you canât discuss a logical problem without emotions then thereâs nothing to discuss, only argue, which I have no interest in.
youtube.com/watch?v=WrjwaqZfjIY
You have no idea what a function is. Iâll give you the 7th grade definition:
Numbers are numbers. 3/1 is not a function, it is a number. 3/1 = 3 is an equation. 3/x = y is a function. The solution to the algebraic equation 3/x = 1 is 3.
A function doesnât need time to work, it just needs an input. The input could be time, or it could be distance, or pressure, or just another number.
Now, what youâre saying about freezing time and thus ending existence is another subject. If we donât exist, then we canât do math, fair enough. Probably numbers wouldnât exist, either. However, if you were to just freeze time within existence, irrational numbers would still be infinitely long. Math is a self-contained language within existence, whether made by man, made by nature, or as manâs convenient way of representing a language made by nature.
Final semseter of mechanical undergrad coming up. I saw your profile, are you still a student?
Yup, first semester of the first year. Pretty stressful stuff here in england since they specialize straight from the beginning and I got my Jan tests next week. Iâm mechanical too. Having some trouble with the electrical and dynamics since I got a normal American diploma. Did you do a placement year? Is it worth it? You applied anywhere for work yet? I did mechanical so I would have a wide range of job options but I have yet to meet final year students and post grads to see what they think. Whatâs your final year project by the way?
Engineers rock
I got an EE/CE degree
What you posted isnât a refutation of what Iâm claiming, period. Youâre confusing ONE definition of function with the general term FUNCTION (to exist, to calculate, to recurse), Iâm using it in the 2nd sense.
You just are not getting it. In order for you to caclulate in the real world you need time, energy to flow, and mass or enregy to make the DISTINCT OBJECTS, each distinct number, and its vectors, out of, you canât create numbers without
- a vector space location to put the number
- stuff to make the number out of (atoms, energy, whatever)
- Time to calculate and create and position the next number.
- And a vector location and a vector space for the number to be bounded in so that it is distinct from all other numbers and positions
Iâm not saying we need âtime to count digitsâ, Iâm saying you need TIME TO CREATE THEM, an infinite series, each digit is being created and calculated
Pi is calculation and all calculations can only take place in time, if we froze time, you being a time bound being, you could no longer create the next number in the sequence, so the sequence gets frozen in the frame.
Time changes values, lastly you are just incapable of comprehending what Iâm saying because youâre still under the false assumption that numbers are made of non-existence, they arenât, they are made of stuff in the real world, in your mind they are still made of stuff (patterns of matter and energy).
Youâre still under the illusion that numbers are âseperateâ from nature, they are merely descriptions of geometry, if you represent all the digits of pi as shapes, you would see the shapes expanding and growing, and that growing stops once time stops. Thatâs all the proof one needs: the Logic of geometry shows your thinking is deeply flawed.
There is a reason why there is computational limits on pi on a computer: A computer eventually runs out of memory to store the digits, this is why I made the statement, if you froze time the function (endless series) would stop, since the function to create the next digit itself would have stopped as well.
Iâm going to go even further and define what I really mean: Stop the flow of energy and time all at once, therefore energy would no longer be flowing either, it would be âfrozenâ as well, and therefore itâs function would be held in stasis.
Youâre right I donât get because you are contradicting yourself. You say you need â3) Time to calculate and create and position the next number.â
Then you say âYouâre still under the illusion that numbers are âseperateâ from natureâ.
If numbers are not separate from nature as you say, meaning they already exist and are not merely a human description of nature, then why would we need time to calculate them? You saying that we, as humans, calculate these numbers implies that they are of our own creation. Nature does not calculate numbers, we do. Since numbers are a human concept used to describe the things we see in nature, time is a non-issue.
Your computer analogy is flawed. Does the ratio between a circleâs diameter and circumference not exist until a computer calculates it? Or is it something that exists that takes time ONLY for us to describe it as we see it? Just because a computer uses time and memory to describe this ratio, does not mean that it does not already exist in itâs fully infinite form. And furthermore if time were stopped, it would still continue to exist in that same form, even though we may lose the ability to fully count it. Do you seriously believe that if a computer ran out of memory after 2 billion digits of pi that pi would then suddenly be a rational number for that computer?
Mabye you should read my whole post:
I happen to believe math is a kind of built in quality of the universe. But that doesnât mean we havenât taken it and created a self-contained language apart from nature, and it doesnât mean that simply stopping time, keeping everything else the same, changes the value of any number. Does it change the value of 3? If not, it wouldnât change the value of pi. Pi is always there, itâs always the same thing, we just calculate it as a function. It is a number that is described as a function. Itâs pre-existing; each decimal place has an absolute value before we start to calculate it.
Thatâs your biggest issue. Pi isnât a calculation. Donât believe me? Whatâs the circumference of a circle with diameter = 1? Oh snap, now piâs a distance.
Engineers: 1
Not engineers: -pi
I am viewing this thread a little late and I may have missed something, so correct me if Iâm wrong, butâŚ
What is meant by a âdiameter = 1â? Is that one inch, one meter, one mile?
Pi * 1 Inch, equates to Pi * 2.54 cm, doesnât it?
In all practicality, wouldnât engineers or mathematicians just change the units of measure if they ran into this problem? Doesnât this actually happen all the time?
He was trying to make the point that pi is just an irrational number, not some function. You are right, and I said earlier, if you multiply any irrational number by a rational number, the result will still be irrational, so it makes no difference what unit of measure you use
I meant it as just 1, with no units, but it doesnât matter if you gave it units. The relationship between circumference and diameter is always the irrational number pi if you keep the units the same on each.
Is the universe made up of fundamental particles, or does it boil down to equations of energy?
If itâs fundamental particles, then everything is natural numbers.
If itâs equations of energy then yes itâs only irrational numbers. Mind you- these are not numbers that are impossible to describe they simply have to be described with a numerical pattern (which might everntually become a consistent pattern) rather than a rational number.
My real question is- will the universe ever churn out a consistent pattern with no exception? Maybe not.
^^ I fail to see how. Properties and interactions of single entities can have complex relationships involving irrational numbers.
How many legs does a cat have?
the square root of two isnât irrational due to the input of something external called spaceâwhile geometry is an epistemically interesting concept to integrate into math, requiring thought about what axioms need be added and why, itâs really still just a simple, mathematical, formal system with no âmessyâ input, not when youâre just âmeasuringâ (calculating) the diagonal of a square. the difference between that kind of irrational number and the kind of irrational numer youâd get from the actual measurement of something is that even that kind can be encoded in a finite way with exactitude. just say 2**.5, or even specify the algorithm for expanding that in decimal form, rather than trying to specify the decimal form itself, and there you have a simple, finite, and exact way to represent the value, which means no input from any particular measurements.
space doesnât even exist as a thing-in-itself. trying to get input âfrom spaceâ is like trying to make something from nothing. if space existed as a thing-in-itself, there would be some way that it, in itself, could, in principle, affect us⌠and as it is, we only know of and measure âspaceâ as an abstraction over measuring material objects.