The equations are a mathematical model. You claim they are exact reality, but of course that is a metaphysical position with considerable evidence against it. Equations are historically contingent and always subject to revision.
Can "Infinity" ever be more than a mathematical abstraction?
- Thread starter Seattle
- Start date
The equations are a mathematical model. You claim they are exact reality, but of course that is a metaphysical position with considerable evidence against it. Equations are historically contingent and always subject to revision.
Which has nothing to do with the mathematical fact of the matter.
What is a computable infinity? You seem confused on the basic definitions.
Last edited:
The infinite sum of distances abstracted as 1+1/2+1/4 - - - - = 2. You've seen that example of a mathematical infinity with a physical analog or pair, offered as a way of keeping it simple here, four times now in this thread.
Again: please attend to the topic of the thread. Your mathematical facts are distracting you from the matter at hand.
Countably infinite and computably infinite are the same thing. An algorithm that computes the natural numbers is pretty simple.someguy1 said:
Except for equations like F = ma, or $$ E = \hbar \nu $$?
Maybe $$ E = mc^2 $$?
Last edited:
You are entitled to your own opinion but not your own facts. You're just making things up. Countably infinite is a standard technical term. "Computably infinite" you will not find anywhere.
Sorry to trouble you with facts. I can see how they'd confuse you.
I don't even know what this argument is about but I found "computably infinite" on Google.
Here's one example of its use:someguy1 said:
https://math.stackexchange.com/ques...tree-with-no-computable-infinite-branches-usi
I'm happy for you that you found some guy on Stackexchange using the phrase. I don't think this convo's productive anymore as you're ignoring the substantive issues and have not addressed the many contradictions in your own statements. All the best.
Last edited:
They aren't troubling, they are irrelevant. You have wandered off the topic.
You said this about equations in physics:someguy1 said:
There is considerable evidence that F = ma isn't exact? The equation (not a measurement of mass or acceleration), is subject to revision?
Equations aren't reality, but equations with physical constants in them must say something about reality, surely? Avogadro's number cannot be approximate, although we only know 9 significant digits, there cannot be an approximate number of atoms (or anything else) in this constant. Likewise the speed of light cannot be approximate, Newton's constant can't be either.
Have you noticed how F = ma says nothing at all about measuring any of F, m, or a? Although you can do this in experiments, the results won't be exact (although the equations are).
It's a definition. Are you completely unaware of that fact? Like I say, I'm done here. If you go back a few posts and start engaging with any of the substantive points I made, or clarifying the various contradictions in your own claims, I'd be happy to dialog. As it is, none of this is productive.
F = ma is a definition. It can't be true or false.
At this point I've wandered off the thread.
Last edited:
Speakpigeon
Valued Senior Member
Sure, but you don't know the decimal expansion of a non-computable so what is it that you know about a non-computable number that proves it does not amount to a rational? Maybe the decimal expansion of pi repeats itself at some point. Why not?
EB
Because a high school student can prove that a real number is rational if and only if its decimal expansion eventually has a repeating block. It's a very simple proof, in fact the proof is based on the grade school long division algorithm.
Write4U
Valued Senior Member
If the sequence is infinitely long, there will come a point where the sequence repeats. It has an infinite length to work with....
Speakpigeon
Valued Senior Member
Do I have to state the obvious?! You're just being awkward.
How much do you have to go in a very, very long division before you're allowed to give up and just admit I don't know?
If pi was a rational number with a repeating sequence 10 to the power of 10000000000000000000000000000000000000000000000000 long then no one would know. "Pi has been calculated to over one trillion digits beyond its decimal point". Probably impressive but not enough to conclude.
If all you have to go by is the division algorithm, then you can't conclude meaningfully that any number is non-computable. All you can say is that it's not computed yet.
Oh, wait, I know, you don't understand what "computed" means! Sorry, I forgot again you just don't speak English...
EB
Speakpigeon
Valued Senior Member
No, not necessarily. There has to be bits that are repeated but then they can be mixed together to form longer bits that won't be a repeat.If the sequence is infinitely long, there will come a point where the sequence repeats. It has an infinite length to work with....
0.13
0.1313
0.131313
0.131313134131313
0.1313131341313131313131341313135
0.131313134131313131313134131313513131313413131313131313413131357
etc.
There is always a sequence long enough to not repeat previous sequences since there's no limit to the length of the new sequences.
EB
I read this post and totally understood where you were coming from. I was just about to write you a clear explanation of what it means for a number to be computable, and why every rational satisfies the definition. All I'm doing is telling you about one of the ideas in Turing's 1936 paper in which he invented the Turing machine and founded the field of computer science. We know exactly what it means to be able to compute a real number, because Turing explained it to us. And I had in mind to explain it to you, simply and clearly with examples, so you'd learn something.
Then I got to your obligatory personal remark, and I just said to myself, "Fuck it."
Have a nice evening brother.
Last edited: