Anyone here into math?

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These days and in the future AIs solve things better than cleverness using:

https://en.wikipedia.org/wiki/Monte_Carlo_method

 

I don't believe that Eurika moments ever involve more complexity. Typically they involve being able to simplify them using different coordinate systems. (topological projection)

 

Many very clever people for thousands of years had all kind of 'truths' about the strange orbits of the planets.

It took a very simple coordinate shift ( Heliocentrism ) to make what clever people were certain of, in to something a child can correctly understand.

[Guest [ch...]]

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i have heard of dedekind cuts but i do not know what they are. yet i can say that your understanding that dedekind cuts can generate irrationals is wrong. like chessplayer, you are only misunderstanding sites and texts.

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That's like saying "I don't know what meatballs are, but I know they cannot be used to make meatball soup".

 

(I have a degree in mathematics from Harvard, so I don't think I'm "only misunderstanding sites and texts". )

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I am curious If meat ball soup is actually possible... ??

[Guest [ch...]]

I am curious If meat ball soup is actually possible... ??

Not sure if that was a serious question, but here's a recipe https://www.tasteofhome.com/recipes/swedish-meatball-soup .

 

Then again, meatballs have a volume of 4/3 * Pi * r^3 where r is their radius, and since Pi is irrational, meatballs must be irrational, so they require an uncountably infinite amount of meat, making it formally undecidable whether I should have meatball soup for lunch...

[Guest [Kp...]]

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i have heard of dedekind cuts but i do not know what they are. yet i can say that your understanding that dedekind cuts can generate irrationals is wrong. like chessplayer, you are only misunderstanding sites and texts.

...

 

That's like saying "I don't know what meatballs are, but I know they cannot be used to make meatball soup".

 

(I have a degree in mathematics from Harvard, so I don't think I'm "only misunderstanding sites and texts". )

 

here is the definition of irrational from wikipedia - In mathematics, the irrational numbers are all the real numbers which are not rational numbers, the latter being the numbers constructed from ratios (or fractions) of integers.

 

if the dedekind cut (or ANY cut or algorithm) can generate an irrational, then why can i not express the irrational as a fraction by dividing it by 1? if you can generate an irrational, it ceases to be irrational.

 

is that convincing?

 

i graduated from columbia.

[Guest [Kp...]]

chessplayer, i have a very easy way of convincing you. i am sure you are familiar with cantor's diagonal slash. i can show you that you are wrong in just 2 steps if you like.  diagonal slash is probably the simplest proof in math. yet it is the most hard to understand. we read it and think -- this is child's play and so obvious, ok let me move on to the next chapter. but very few actually understand it, yet everyone thinks he does.

[[Rr...]]

Intelligent men 

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I think the meat ball soup problem could only be rational if the was a phase transition in the meatball form solid to a more liquid form. Only problem with this theory is there would be no balls of meat in the soup. So it's premise could not  be justified. I am also pretty sure that pie are round.

[Guest [Kp...]]

I think the meat ball soup problem could only be rational if the was a phase transition in the meatball form solid to a more liquid form. Only problem with this theory is there would be no balls of meat in the soup.

 

you are wrong because you will have neither meat balls nor soup. you think of liquid as continuous but continuums cannot exist (only discrete objects can) and if you are eating the soup, i am pretty sure you would be eating something that exists so the soup cannot be liquid and continuous and exist.

 

hey, i'm kidding, lol, but what i said is right you know. 

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I'm unconvinced by the images of meatball soup that can be found on the internet. Most of them look photoshopped if you look closely. I would require a more rigorous proof which I can't see being possible without motive.

[Guest [Kp...]]

I'm unconvinced by the images of meatball soup that can be found on the internet. Most of them look photoshopped if you look closely. I would require a more rigorous proof which I can't see being possible without motive.

 

how about this one? i'll assume i am cantor -

 

hypothesis - liquid continuums like soup cannot exist in nature

 

proof by contradiction -

 

let us assume that continuums exist in nature

then zeno's paradox exists in nature

but we know that zeno's paradox does not exist in nature

 

thus liquid continuums like soup cannot exist in nature. 

 

i'll take one bowl of meatball soup as remuneration for this proof please. 

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let us assume that continuums exist in nature

Is nature not quantized at the plank length ?

 

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There is high probability that meatball soup in a parallel universe. But has any one every really seen it 1st hand, or even a sweed for that matter. Swedish people also look badly photoshoped.

[Guest [Kp...]]

let us assume that continuums exist in nature

Is nature not quantized at the plank length ?

 

it probably is. but there is more to it. (science fiction ahead) the infinitesimal may be dynamic. that is a very contradictory thing i said but considering that every thing in the universe is relative to each other, including space, the planck length of the diagonal of a square and its side might always be rational and we might have no way of imagining this just as we have difficulty imagining that at infinite speed, c, there exists no distance. but then the universe will become countable and probability and randomness and free will not exist. even consistency might not exist. so it's between rock and a hard place.

[Guest [Kp...]]

But has any one every really seen it 1st hand, or even a sweed for that matter. Swedish people also look badly photoshoped.

:D after all these hundreds of years, we find we are back to cartesian solipsism?

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I don't think Donald Trump agrees much with Solipsism. Did some German aristocrat invent it.

[Guest [Le...]]

There is high probability that meatball soup in a parallel universe. But has any one every really seen it 1st hand, or even a sweed for that matter. Swedish people also look badly photoshoped.

 

Since I’m 50% Swedish and of the belief that we are all gorgeous whether photoshopped or not, I’m just gonna toss this out here.

 

Italian Wedding Soup

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With only 50% and (Italian) Meatballs IN soup, I don't think we can jump to conclusions.

[Guest [ou...]]

i would not have participated after that point had you not made an untrue statement about irrationals.

that i do not want to learn anything more about numbers

does not mean i am unwilling to teach what i already know about numbers.

 

Every statement I made is TRUE and there is proof.

Some of the things you 'know' are false and

your unwillingness to learn more prevents you from seeing that.

 

i studied godel in college and i had thought i understood it but i hadn't.

i understood it thirty years later.

godel proved that logic was "consistent and incomplete."

you haven't accepted that "you are having difficulty."

 

You are the one having difficulties, even with Godel.

He did NOT prove that logic is consistent and incomplete.

He only proved that it can be either consistent or complete but not both.

We chose incompleteness over inconsistency.

 

when you say that a function on the natural numbers using dedekind cuts can generate an irrational number,

then you are saying that irrational numbers are turing computable.

if irrational numbers are turing computable,

then turing is wrong because turing said that some algorithms are not turing computable whereas

you are saying all algorithms are turing computable.

 

Here you misunderstood every single thing I said.

First of all, the Church–Turing thesis is just that, a thesis which could be false.

 

here is the definition of irrational from wikipedia -

irrational numbers are all the real numbers which are not rational numbers

 

Did you see the word DEFINITION anywhere?

That's because this is NOT their definition, rather a consequence of it.

We use subtraction on the natural numbers to construct/define integers.

We use division on the integers to construct/define rational numbers.

We use Dedekind cuts on rational numbers to construct/define the real numbers NOT compute them.

 

Regarding computability I was talking about some numbers (pi in particular).

The real numbers are uncountable so most of them are not computable

but ALL algebraic numbers (like √2) and many transcendental numbers (like pi) are computable.

When we say a number is computable we mean that it can be computed

to within any desired precision by a terminating (finite) algorithm.

What you seem to be talking about is HYPERcomputation which appears to be impossible in our universe.

For that one needn't invoke Godel or Turing just Einstein and his cosmic speed limit (that of light).

 

Now I know infinity can be perplexing as nothing in nature is truly infinite,

so here is a finite compilation of mathematical facts about infinity:

 

1. Rational numbers are countably infinite.

2. Irrational numbers are uncountably infinite.

3. Whether there exists a set with cardinality between A0 and A1 remains an open problem.

4. There are countably infinite cardinal numbers.

5. An infinite sum of integers might not be an integer (1-1+1-1+...=1/2).

6. An infinite sum of rational numbers may be irrational (1-1/3+1/5-1/7+...=pi/4).

 

continuums cannot exist (only discrete objects can)

 

Is there any DEFINITIVE proof of that I don't know about?

 

PS: I have a diploma in Applied Maths & Physics from the Athens Polytechnic,

not that degrees mean anything by themselves.

One must 1st learn how to think and then be willing to abandon ANY belief given sufficient evidence.

If the above do not suffice I don't think I can be of any more help.

[Guest [Kp...]]

i have recieved a pm from chessplayer. i am reproducing it as the matter is escalating -- I have reported your post to the moderators who will likely remove it. You are becoming verbally abusive and will be kicked out of the forum again if this behavior continues. (You are also very confused about math.)

 

i apologize to both of you, chessplayer and outis, if you have found my posts verbally abusive. i will henceforth try to be more polite and civil. also, i agree that you both are right in your interpretations about irrationals. you both are more educated in math than me. i leave it to the moderators to take whatever step they wish to take  to avoid such incidents in future.

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OMG 

I wish people would remain on topic.

 

[Guest [Le...]]

i have recieved a pm from chessplayer. i am reproducing it as the matter is escalating -- I have reported your post to the moderators who will likely remove it. You are becoming verbally abusive and will be kicked out of the forum again if this behavior continues. (You are also very confused about math.)

 

i apologize to both of you, chessplayer and outis, if you have found my posts verbally abusive. i will henceforth try to be more polite and civil. also, i agree that you both are right in your interpretations about irrationals. you both are more educated in math than me. i leave it to the moderators to take whatever step they wish to take  to avoid such incidents in future.

 

Kpin/V, please take moderation issues up at the Helpdesk. Since you already deleted the offensive post, you clearly knew it was out of line.

 

Normally I wouldn’t respond publicly in the thread, but since you kicked the door open . . .

 

Now, please let this thread return to the topic of math and, apparently, meatballs.

[Guest [ch...]]

BTW that PM was in response to a post of kpin's where he went on for a few paragraphs about how ignorant I am and concluded with "listen to your seniors, you sophomore". I reported the abusive post to the moderators, and it is no longer present.

[Guest [Kp...]]

Kpin/V, please take moderation issues up at the Helpdesk. Since you already deleted the offensive post, you already knew it was out of line.

 

yes, i deleted it because it was out of line. i apologize. i will exercise more restraint. thanks!

[Guest [Kp...]]

BTW that PM was in response to a post of kpin's where he went on for a few paragraphs about how ignorant I am and concluded with "listen to your seniors, you sophomore". I reported the abusive post to the moderators, and it is no longer present.

 

i was upset then although that is never a good reason for doing anything offensive. i have sobered down. let me know if you wish to take up the cantor challenge. i will respond to outis in a while. i feel our differences (outis and me) have considerably narrowed down but still a few issues remain. one of us would understand cantor right by the end of all this and it could be me!