There are no rational numbers in nature

Could you explain why an irrational number is a function or at least point somewhere for more info? I’ve never heard that before. How can it be a function of time? The value of pi is not rational, and it does not change with time, so how would stopping time suddenly make the value rational? The definition of an irrational number is a negative one, meaning that irrational numbers are defined as any real number that is not a rational number. There are an uncountable number of irrational numbers.

Ah, I see your issue. It’s a function, but not of time. Infinte series work off a generic variable, call it whatever you like, but it’s not time. Freezing time, whatever that would mean, would not change the value of an irrational number, or stop it in it’s tracks.

You guys are both right. I think my OP title was a little too grandeose. I think it should have read “there are no rational numbers in space” since it has more to do with geometry than countable objects. In other words, my argument works better with quantities that describe “how much” of something there is (like distance, angle, volume, anything spatial, etc.) as opposed to “how many” there are. And I guess you could put all these things in terms of units so that a question of “how much” volume there is can be rephrased as “how many” cubic feet there are, but I think the point here is that you might still end up with an irrational number even when measuring a certain number of units, but not necessarily. When you stick strictly to the “how much” terminology, it is necessary (not logically, but practically).

Well, by definition, measurement is an estimate. Any real scientific measurement includes not only the estimation itself (length, mass, etc), but also a margin of error, and measure of confidence.

Think of it this way, if knew the value we were looking for, we wouldn’t have to measure it, would we?

I wonder if the quantum length would come into play at some point and stop the irrationality of a measurement. But, for all intents and purposes, I’d say you are right; measurements are irrational numbers. The probability that a measurement just stops at a certain point, like 2.1231231490551340980134810329841240000000000 meters seems unlikely.

And that is where you are incorrect, we are talking about numbers made of stuff, you can’t have a number that is not made of something, when you think of a number it is made of concept-data, therefore, in order to calculate you have to be made of something, you can see this by grabbing some playdough and creating numbers out of it, once you run out of playdough you cannot create more numbers.

You’re still under the mistaken idea that math exists ‘apart’ from nature, when math is nothing more then a description of geometric structures. Again all calculation requires time, and if you represented and irrational number in binary the binary string would be growing, and each bit in the string needs a vector and location in space to be stored, if you stopped time that growth function would stop, period. So no, it has everything to do with time, if we froze time all calculation would stop.

Do you know anything about calculus? An irrational number just exists, it’s only the calculation that requires an effort on our part. Freezing time does nothing to the number. You can say that you only want to take the first ‘n’ terms of an infinite series, but that has nothing to do with time.

Here, this video should sum it up for you: youtube.com/watch?v=WrjwaqZfjIY

This was a thought that actually occured to me a few years back and I’m glad I’m 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 there’s 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 “speed(units/time)”, which seems to be your assumption superculture.

Thanks Rouz :slight_smile:

Yes it does, but I think the number of particles falls into the “how many” camp as opposed to the “how much” camp. When it really comes down to it, I think the “how much” camp can be reduced to only continuous quantities such as space and time (in other words, not discrete “things” that exist).

What you’ve said still doesn’t 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 you’d 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 it’s opposite 3/1 is a function and since even “irrational” 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 ‘stuff’ to make numbers out of. Numbers are not made out of non-existence, they are made of stuff that exists.

What you’ve 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 you’ll 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 can’t grasp what I am saying and it is not an assumption it is a fact, you can’t 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 ( :astonished: quantum physics is crazy). It’s murky ground still, but the point is we can’t get exact measurements because we still don’t 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 don’t have to exist in nature, only in our heads, and if that’s the case, then there is no reason to limit them

Always good to see the products of an engineer’s mind :stuck_out_tongue: 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 won’t be emitted randomly, as far as I’m aware. Measuring them in a hypothetical scenario still makes sense, we just don’t have any equipment to measure something to that smallest possible point. I’m assuming there is a smallest fraction. Perhaps something like an Avogadro’s 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, we’d end up with a rational number.
I used to think of the possibility of “smallest possible movement” by any particle which would imply that a particle can only move 0.00…1m at a given time and not 0.00…05m to rationalize movement as finite as opposed to infinitely small. Possible?

If self-righteousness and emotionally triggered insults were indicators of being correct, you’d be have the final say. Numbers are concepts. You’ve said “if you were to expand an infinite series, it would take up all matter in the universe pretty quickly”. We’re saying it doesn’t do it “pretty quickly”, it doesn’t have time. Two infinites don’t reach a given number at different times, infinite doesn’t work with speed, it isn’t a number, it’s a concept and it’s irrelevant to time. Freezing time doesn’t let you count [x/0] or pi, assuming you weren’t frozen. Pi will be irrational at 0 time or at infinite time.

You’re assuming that things are constantly growing in time as one goes to smaller measurements. I assure you they aren’t. 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 won’t change regardless of how small you go. Freezing time is irrelevant.
Saying something is bullshit just shows that it opposes your views and that you’re disrespecting the person due to an inability to present a viable argument. If you can’t discuss a logical problem without emotions then there’s nothing to discuss, only argue, which I have no interest in.

youtube.com/watch?v=WrjwaqZfjIY

You have no idea what a function is. I’ll 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 doesn’t 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 you’re saying about freezing time and thus ending existence is another subject. If we don’t exist, then we can’t do math, fair enough. Probably numbers wouldn’t 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 man’s 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. I’m 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. What’s your final year project by the way?

Engineers rock

I got an EE/CE degree

:smiley:

What you posted isn’t a refutation of what I’m claiming, period. You’re confusing ONE definition of function with the general term FUNCTION (to exist, to calculate, to recurse), I’m 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 can’t create numbers without

  1. a vector space location to put the number
  2. stuff to make the number out of (atoms, energy, whatever)
  3. Time to calculate and create and position the next number.
  4. 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

I’m not saying we need “time to count digits”, I’m 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 I’m saying because you’re still under the false assumption that numbers are made of non-existence, they aren’t, they are made of stuff in the real world, in your mind they are still made of stuff (patterns of matter and energy).

You’re still under the illusion that numbers are ‘seperate’ 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. That’s 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.

I’m 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 ‘frozen’ as well, and therefore it’s function would be held in stasis.

You’re right I don’t get because you are contradicting yourself. You say you need “3) Time to calculate and create and position the next number.”

Then you say “You’re still under the illusion that numbers are ‘seperate’ from nature”.

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 circle’s 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 it’s 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 doesn’t mean we haven’t taken it and created a self-contained language apart from nature, and it doesn’t 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 wouldn’t change the value of pi. Pi is always there, it’s always the same thing, we just calculate it as a function. It is a number that is described as a function. It’s pre-existing; each decimal place has an absolute value before we start to calculate it.

That’s your biggest issue. Pi isn’t a calculation. Don’t believe me? What’s the circumference of a circle with diameter = 1? Oh snap, now pi’s a distance.

Engineers: 1
Not engineers: -pi