/sci/ - Science & Math

(((Real))) numbers aren't as real as they claim to be

>>15113246
No human mind 'computes' irrational numbers, they're used symbolically according to their definitions, and any CAS can 'deal with them' that way

>>15113278
>No human mind 'computes' irrational numbers
Only NPC and low IQ can't do it.

>>15113272
kys

>>15113283
Go ahead and compute it then, post result

>>15113246
Get yourself a symbolic calculator. Bam "hyperturing" computer
(Being computable is a property required to do precise numeric math only, wich jsut happens to be the most convenient and ressource efficient way computers work, but "not computable" doesn't imply computers can't deal with it at all.

You can do math with real numbers just fine using analog circuitry. It's just less precise than floating-point arithmetic.

What where you trying to write with all these single letter image threads?

>>15113300
>some people coincidentally use well known mathematical symbols on a math board
>this somehow is a conspiracy following a master plan to write a secret message
Sure thing, schizo. Are you seeing patterns again nobody else sees? Try talking to a doctor.

>>15113246
>Is this proof that consciousness is hyperturing?
Yes. The awareness itself is not a algo and non-physical and not a creation of computation. The CONTENT of the of the consciousness, ie the physical datastream that the freewill awareness unit (consciousness) interfaces with is a computed/informational/numerical/virtual reality. It's a computed reality that includes consciousness as an input device I might add. So it's not a situation of pre-determination on what will happen. Though the majority of macro objects with relative low uncertainty such as planets' orbits are EFFECTIVELY (from the view point of the observer) deterministic. It's an probabilistically evolving simulation from initial conditions of data objects (matter) and rules on how they interact (physics 'laws'). And, by the way, the system can be updated between planck refresh rate. To the renderer, the 'time' between refresh is not physical. This is why you can mimic some of the content of consciousness, but never create it, ie, never create a a free will awareness unit. The only way computers might ever be conscious is if a free will awareness unit is either assigned to a non-bio-computer to use as an avatar, or a freewill awareness unit CHOOSES to use one. OR, there might be a constraint that says there can only be bio/metabolizing avatars. We (those of of consciousnesses immersed in the system of physicality) don't remember pre-existence and the avatar choosing/assigning process, at least I don't. The info data base is out there to query to find out, but I myself can't so far. Others claim to have accessed this info. When we are immersed in the reality (birth) there is a memory constraint placed on the observer which makes it hard/impossible to remember pre-existence.

>>15113246
If you are interested in how our probabilistic consciousness based virtual (informational) physical reality works and how the freewill awareness unit (consciousness/player/observer)'s choices fit in to this, see vid here
https://www.youtube.com/watch?v=JMImjFYZ1iY&list=PLQ0PXV3djGQuZJpC99bd6cZIOLnz1BV-w&index=32
He talks slow, so speed it to x1.5
So every Δ of planck time, a random draw from a prob distribution of possible future outcomes is drawn then update. Of course, some outcomes are more probable than others. So the sun is going to continue on it's EFFECTIVELY deterministic course. There is some non-zero chance that it will tunnel across the universe from one refresh to the next delta t of time.

>>15113246
>yet the human mind can easily deal with non-computable numbers
What's that supposed to mean

Or said differently: This doesn't mean anything

>>15113246
>yet the human mind can easily imagine that it's able to deal with non-computable numbers
FTFY
>>15113272
Nothing jewish about real numbers. Goyim love them as much as anyone else. And most finitists have been jewish (Wildberger, Zeilberger, Kronecker, Goodstein).

>>15113246
>the human mind can easily deal with non-computable numbers
Can I have a demonstration?

>>15113246
>love cannot be encoded on a computer
Is this proof that consciousness is hyperturing?
>the idea of invisible fish is not Turing computable
Is that also proof that consciousness is hyperturing?
>>15113283
Compute e+pi. I'll wait.
>>15113296
Please use analog circuitry to resolve the riemann hypothesis and collect your Fields medal. I'll wait.
>>15113378
You cannot justify any of your claims that you put forth so pridefully.

>>15113538
I am not op, but I took it to mean 'conceive of'. And of course, computers can't conceive of anything, because they are not aware. In before
>this is not true, humans are computers and they are aware
This is question begging. It's just re-stating the premise (if your premise is that humans are computers) as the conclusion.

There's also unreachable countable ordinals (anything past the Church-Kleene ordinal), which, despite being countable, no finite amount of symbols can represent them.

>>15113545
Not any of the posters you replied to, but I just find it remarkable that you manage to put forward a low IQ take on every post.

>>15113545
>Compute e+pi. I'll wait.
e+pi = 2+3 = 6

>>15113562
The Riemann hypothesis post flew over your head, didn't it. If not, please explain what I meant by that? Why would you be able to solve the riemann hypothesis if you can do math with real numbers?

>The Riemann hypothesis post flew over your head, didn't it. If not, please explain what I meant by that? Why would you be able to solve the riemann hypothesis if you can do math with real numbers?

>>15113246
>yet the human mind can easily deal with non-computable numbers
It cannot. Where did you get this idea?

>>15113697
Name one thing one could do to a non-computable number that I can't do in my head right now. Protip: you can't.

>>15113741
Given a formula for computing any number, you could not compute it

>>15113561
Another fantasy, like invisible aliens that live in castles or like santa claus. It's time to grow up.

>>15113750
Computing a non-computable number is a contradiction. I said:
Name one thing one could do to a non-computable number that I can't do in my head right now.

I can compare an uncomputable number with a computable number. For example I can say that an uncomputable integer between 6 and 7 is greater than 3. A computer can't do that because it can't represent said uncomputable number in the first place.

>>15113856
>an uncomputable integer between 6 and 7 is greater than 3
>it can't represent said uncomputable number

typedef struct Noncomputable { int min, max; }
bool greaterThan(Noncomputable x, int y) { return x.max < y; }

Seethe.

>>15114005
Doesn't work when y is between min and max.

>>15114012
If y is within thembo range, there's no way to know if it's greater or smaller. Lurn2logic. I'll admit the function name is misleading, though.

>>15113246
>>yet the human mind can easily deal with non-computable numbers
On a conceptual level. But the uncomputables have an endless representation, meaning you'd need some kind of infinite consciousness to be able to treat them. I.e. god.
Since statements about god aren't very interesting, we are back at where we started that uncomputables are equally inscrutable to ordinary consciousness.

>>15113246
Only "computable" real numbers exist.

>>15113396
Planck time and the rest of modern cosmology is nonsense. Your model doesn't work so you posit "dark energy" and "dark matter."

>>15113659
[math] 3.2>\pi>3.1, 2.8>e> 2 [/math] so [math] 6>\pi+e> 5.1 [/math]. Therefore you have not calculated [math] \pi + e [/math].
Moreover [math] 2+ 3 \not= 6 [/math]. 2+3 =5

>>15114164
>Planck time and the rest of modern cosmology is nonsense
No, it isn't there are perfectly good reasons for thinking that all of the planck units exist, see pic and link.
https://arxiv.org/pdf/1001.1205.pdf
Even if there wasn't and there is a finer resolution, the theory still holds. Are you claiming that there is infinite resolution to the universe? How would you even scientifically verify this? It's not as if you could probe down to some point and say 'here it is, we found infinite divisibility!'. There would always be an infinite amount more of divisibility. Same thing with any claim of infinite anything in the universe. There's no way to varify infinite ANYTHING empirically and so this is just a metaphysical claim. As far as modern cosmology, I agree that most of it is non-sense, but I would argue that the reason is that the cosmologist have a metaphysical BELIEVE in physicalism and materialism and so they try to squeeze the observed data into a physicalist worldview.

>>15113545
2 < e < 3 and 3 < pi < 4 so 5 < e+pi < 7
2.7 < e < 2.8 and 3.1 < pi < 3.2 so 5.8 < e+pi < 6.0
2.71 < e < 2.72 and 3.14 < pi < 3.15 so 5.85 < e+pi < 5.87
This can be continued to whatever precision I desire given sufficient computational resources.

no

Real numbers my ass

>>15114170
Uhm sweaty, that's wrong.
2+3 = (2+2)+1 = 5+1 = 6

All numbers are fake

>>15113246
>yet the human mind can easily deal with non-computable numbers
How does it do that? By defining them as solutions to equations, integral equations, etc. i.e. by replacing them with symbols. You can do that on a computer too using symbolic mathematics software. The human mind can't actually compute e*pi or whatever on the fly.

>>15115697
Why are you talking about e and pi? This thread is about uncomputable numbers. E and pi are computable.

>>15115706
Sorry, I thought the thread was about uncompetable numbers. How can other numbers even compete?

>>15115706
ok, whichever numbers

>>15115697
>How does it do that? By defining them as solutions to equations, integral equations, etc. i.e. by replacing them with symbols
Wrong.

>>15115718
Wrong!

>>15113659
Dangerously based.

Not one comment on this thread about how this is bait. Check the catalogue lmao

>>15113246
bump

>>15113246
>yet the human mind can easily deal with non-computable numbers
What are you talking about? Demonstrate that we do arithmetic on the reals by "computing" with them.
Every concrete computation we write down using real numbers either uses a subset of them that are computable or approximates them to a specified precision. Every symbolic computation relies on a system of finite rules to manipulate expressions or reason with quantity.

When you demonstrate that the reals have the Archimedean property, you aren't doing computations on the reals. You're using the properties of the reals to assert something about them.

>>15114263
Planck time/scale are just numbers from a model. A model you have proven with the rest of your post that you don't understand. The most it is is a statement on contraints of human measurement when it really is just a constraint on a model. It's along the same lines as the uncertainty principle and statistical approach of quantum mechanics. There is no physical implications from this other than at most constraints on the ability of human beings to make measurements. This does not justify any assertions about the nature of space or time.

>>15114306
He said compute not approximate.

π is the proof we live in a simulation

>>15113674
Low iq post

>>15117212
I define real numbers to be sequences like that.

>>15114306
Spoiler: a computer can do that too

>>15117507
Obviously so, since e and pi are computable numbers.

>>15117394
>π is the proof we live in a simulation
/thread

>>15113278
>>15113545
You can be disregarded solely on the fact that you do not know what non-computable numbers are. They don't have an algorithm which can compute them with any precision. Most numbers are not just non-computable, they're also undefinable, meaning that you can't access them with language.

>>15113293
>>15118146

>>15118146
>Most numbers are not just non-computable, they're also undefinable, meaning that you can't access them with language.
Why do you think these numbers exist?

>>15118165
He's gay and wrong. They're "definable", there's just no finite algorithm that can give you any numerical value.

>>15118165
>Why do you think these numbers exist?
It's not me, it's how a property of the reals as constructed in mathematics.
>>15118180
No, you're wrong. A number can be uncomputable, but definable like Chaitin's constant. But most numbers are not even definable, since we only have a countable list of definitions.

>>15118461
>most numbers are not even definable, since we only have a countable list of definitions
>since we only have a countable list of definitions
This occurred to me at first, but a grammar for definitions can allow for infinite recursive nesting, so is it really a countable list?

>>15118461
>It's not me, it's how a property of the reals as constructed in mathematics.
But you sound like you consider this construction to be sound.

>>15118468
>but a grammar for definitions can allow for infinite recursive nesting, so is it really a countable list?
Any definition would still be finite. If you allow for "infinite definitions", then yeah all the numbers are "definable" in that sense, just write out all the infinite digits. https://en.wikipedia.org/wiki/Definable_real_number
>>15118486
Sound for what? It's not sound for computer science, but those complications are an unavoidable consequence of the construction of the reals, for they are uncountable, while all the formulas in any language form a countable set. You can't exclude undefinable numbers since the the range of what is definable depends on what language you're using.

>>15113272
/thread
the strongest argument for reals number was created by Enoch and no one gave a fuck because it didn't agree with their precise pedagogical, dogmatic indoctrination.
fucking sad too because Enoch was one to even explain the lain geometry of uncomputable numbers
>best schizo leaves
>left with fucking Tooker
it's over
btw fuck real numbers in general
Enoch's principle of the existence of numbers literally relies on the paradox along the line of "they just do/must"
I mean it's a good use of the anthropic principle, but fuck that
I have no reason to be convinced of anything

The reals? They aren't real.

We don't even know the first digits of a noncomputable number

>>15119162
There is an uncomputable number between 6 and 7 though.

>>15113272
niggas discover nominalism and act like they're schizos

>>15119210
I think the issue here is that it is the PROOF of the existence of an uncomputable number between 6 and 7 that we care about, because that tells us how to parameterize: we need to know the Gödel numbering, for example
so the proof gives us information about how we can go about colonizing the set of uncomputable numbers

Do you believe this Turing machine halts?
I mean, think about it.
It's a matter of belief.
In other words, how are we going to arrive at a common understanding as to whether or not this Turing machine halts?
Remember, when you say
>this Turing machine halts
you're only giving yourself the axiomatic tools and inferential reasoning tools you agreed to at the outset to prove that it halts
so it's really only the Turing machines that halt from the point of view of the context of that axiomatic system, and it isn't necessarily first order logic with ZFC
So if you start with FOL-ZFC and then introduce uncomputable numbers, you're only going to get as far as FOL-ZFC uncomputable

Okay.
Take all of the Turing machines, even the ones that don't halt, and treat them as reporting the value of the n'th digit as the Wiki article says
https://en.wikipedia.org/wiki/Computable_number
If the machine doesn't halt for any value of n, then treat the Turing machine as encoding the value 0.
Otherwise, the Turing machine encodes the value of a real number, a computable real number.
Now enumerate the Turing machines (all of them) and use Cantor's diagonalization argument to find an uncomputable number.
BOOM
I just calculated (computed) an uncomputable number.
Now put that uncomputable number at the beginning of the list, shift all of the computable numbers down one place, run Cantor diagonalization again and
BOOM
I've got two delicious charbroiled uncomputable numbers with a side of fries coming right up...

>>15119260
>If the machine doesn't halt for any value of n, then treat the Turing machine as encoding the value 0.
>Otherwise, the Turing machine encodes the value of a real number, a computable real number.
This gives you a sequence of computable real numbers, but not a computable sequence of computable real numbers. You cannot compute the value of the 37th number in this sequence, for this would require you to tell whether the 37th Turing machine halts. Because this sequence is not computable, neither is the diagonalization you constructed off it.

>>15113246
>yet the human mind can easily deal with non-computable numbers
How?