# Not everything that is true can be proven

#### Delta Prime

Joined Nov 15, 2019
1,311
The most well-known of all the radiometric dating methods is radiocarbon dating (or carbon dating). Although many people think radiocarbon is used to date rocks, it is limited to dating things that contain carbon and were once alive (fossils)

#### MrAl

Joined Jun 17, 2014
9,761
As they say, haste makes waste. I replied hastily, and got wasted..... go you! Goldbach's conjecture of 1742 is fascinating and is likely provable or disprovable not by equation but simply through proof that the algorithm of the equation itself will work infinitely (or won't). How problems are solved is often accomplished by altering the perspective upon which the problem is viewed- this is what geniuses do. They have this remarkable ability to view things differently than anybody else.

Sounds like Conformal Mapping. A different "view" allows a solution to be found.

Are they stating Goldbach's right?
I have read that "Whole numbers greater than 2 are the sum of two primes", but i think it should read:
"Whole numbers greater than 2 can be the sum of two primes". or something like that anyway because 8 can be 5+3 or it can simply be 2+6.
If there is a non sequential solution it may be eventually proved using quantum computing.

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#### xox

Joined Sep 8, 2017
795
The most well-known of all the radiometric dating methods is radiocarbon dating (or carbon dating). Although many people think radiocarbon is used to date rocks, it is limited to dating things that contain carbon and were once alive (fossils)
Sorry, I meant to say "radioisotope dating", as in uranium-lead dating and the like (which can be used to date old rocks).

#### xox

Joined Sep 8, 2017
795
Sounds like Conformal Mapping. A different "view" allows a solution to be found.

Are they stating Goldbach's right?
I have read that "While numbers greater than 2 are the sum of two primes", but i think it should read:
"Whole numbers greater than 2 can be the sum of two primes". or something like that anyway because 8 can be 5+3 or it can simply be 2+6.
If there is a non sequential solution it may be eventually proved using quantum computing.
The conjecture is most likely true (further reading) and to me at least it seems that it will be confirmed not too far in the future either considering the ever-increasing sophistication of modern mathematical analysis tools.

#### MrAl

Joined Jun 17, 2014
9,761
The conjecture is most likely true (further reading) and to me at least it seems that it will be confirmed not too far in the future either considering the ever-increasing sophistication of modern mathematical analysis tools.
Oh i didnt mean to imply that it was not correct, just that i did not like the way it was written in some places. The writing sounds like "Whole numbers greater than 2 can ONLY be the sum of two primes". I realize they did not mean that, but that's the impression one might get by reading the writing of the first statement in my previous post. The second statement makes it more clear that those numbers are the sum of two primes but of course also they can be the sum of other whole numbers too. But i would bet most people read it the way it was really intended. They dont mean that the sum can not be attained some other way too, just that they can always be the sum of two primes.

There are a lot of math problem statements that have not been proved or disproved yet.

#### xox

Joined Sep 8, 2017
795
Oh i didnt mean to imply that it was not correct, just that i did not like the way it was written in some places. The writing sounds like "Whole numbers greater than 2 can ONLY be the sum of two primes". I realize they did not mean that, but that's the impression one might get by reading the writing of the first statement in my previous post. The second statement makes it more clear that those numbers are the sum of two primes but of course also they can be the sum of other whole numbers too. But i would bet most people read it the way it was really intended. They dont mean that the sum can not be attained some other way too, just that they can always be the sum of two primes.

Ah, I see what you mean. Fermat's little theorem is another good example. People sometimes think that it implies that if a number PASSES the test then it must be PRIME. But that isn't the case. In fact it only guarantees that any given number which FAILS the test is indeed NOT PRIME. It's actually pretty easy to see why that sort of thing can confuse people!

#### MrAl

Joined Jun 17, 2014
9,761
Oh ya know what, i didnt realize the video in that first post was THAT video. That has the "Barber Paradox" in it too, one of my favorites from long ago. I havent seen anyone else talk about that in a long time. But that guy does a lot of good videos ive seen other ones he did.

Check out his "Intermediate Axis Theorem" video, a fairly good explanation. I had thought that maybe that was the true explanation why the Shuttle rotated on it's back during the first (and other) takeoffs. If you look around the web you will find that many of the explanations make it sound like they knew all along that it was going to do that when really they did not know until the first flight as i was around at the time watching closely and listening carefully at what they would say caused it and they admitted at the time that they did not know.
But there may be an explanation out there that is compatible with the Theorem mentioned above i didnt do any math yet or anything else too rigorous.
It was interesting that he mentioned that the Theorem was 'hidden' somewhat for years, and when i look back i realize that i had read some very good books on control theory that went into aircraft flight control and related and there was never any mention of this Theorem, something i now view as important in that field.

#### BobaMosfet

Joined Jul 1, 2009
2,063
Sounds like Conformal Mapping. A different "view" allows a solution to be found.

Are they stating Goldbach's right?
I have read that "Whole numbers greater than 2 are the sum of two primes", but i think it should read:
"Whole numbers greater than 2 can be the sum of two primes". or something like that anyway because 8 can be 5+3 or it can simply be 2+6.
If there is a non sequential solution it may be eventually proved using quantum computing.
I have no idea what 'they' are stating, but I may have come up with 2 methods to prove/disprove his theorem. When I get free-time I'll formally write the algorithm and give it a test. I know how far out they've actually tested numbers, but if I'm right, there is a much, much better way to test infinite possibility ranges.

#### xox

Joined Sep 8, 2017
795
I have no idea what 'they' are stating, but I may have come up with 2 methods to prove/disprove his theorem. When I get free-time I'll formally write the algorithm and give it a test. I know how far out they've actually tested numbers, but if I'm right, there is a much, much better way to test infinite possibility ranges.
Sounds interesting. Care to elaborate?

#### MrAl

Joined Jun 17, 2014
9,761
I have no idea what 'they' are stating, but I may have come up with 2 methods to prove/disprove his theorem. When I get free-time I'll formally write the algorithm and give it a test. I know how far out they've actually tested numbers, but if I'm right, there is a much, much better way to test infinite possibility ranges.
Yeah does sound interesting maybe you can make time to write something down.

#### nsaspook

Joined Aug 27, 2009
10,895

#### cmartinez

Joined Jan 17, 2007
7,911
... any mathematical proof must necessarily be a finite set of symbols
sorry, but I don't follow ... and I'm not trying to troll you...

#### MrAl

Joined Jun 17, 2014
9,761
Of course one has to agree with most of that if not all, and it is an interesting video on how we add different things. I just dont like the way it is presented as it sort of borders on a sensationalistic grab line like we might see on the cover of a tabloid or a Huffington Post lead in advertisement or actually many lead in advertisements we see for what are really just a little education usually mixed with lots of advertisements.

For example:
"Guess what this guy did to this giant redwood tree with his bare hand..."
"You would not believe what scientists found in this pile of dung..."
"2+2=5..."

2+2=5 is just a little bit misleading because it suggests we have already accepted the premise that we are doing regular old grade school addition when really that is not the case. So during parts of the video i almost felt the need to say, "No kidding" We all know we dont add certain things while with others we do.

A non sensationalistic introduction would have read more like, "Addition In Physics" or something.

But there are still interesting facts in that video things we dont think about every day.

#### bogosort

Joined Sep 24, 2011
696
sorry, but I don't follow ... and I'm not trying to troll you...
No worries, see if this helps. A proof is fundamentally a deduction, i.e., an ordered sequence of statements (premises) that leads to the conclusion.

Every statement is necessarily a finite string of symbols: we can't read, much less assign a truth value to, infinitely long statements.

Furthermore, a proof must be verifiable: each step in the deduction can be checked to be valid.

Therefore, every proof is a finite set of finite statements, and -- since the union of finite sets is itself finite -- every proof is a finite set of symbols.

Let me know if that explanation didn't hit the mark and I'll try a different approach.

#### xox

Joined Sep 8, 2017
795
Of course one has to agree with most of that if not all, and it is an interesting video on how we add different things. I just dont like the way it is presented as it sort of borders on a sensationalistic grab line like we might see on the cover of a tabloid or a Huffington Post lead in advertisement or actually many lead in advertisements we see for what are really just a little education usually mixed with lots of advertisements.

For example:
"Guess what this guy did to this giant redwood tree with his bare hand..."
"You would not believe what scientists found in this pile of dung..."
"2+2=5..."

2+2=5 is just a little bit misleading because it suggests we have already accepted the premise that we are doing regular old grade school addition when really that is not the case. So during parts of the video i almost felt the need to say, "No kidding" We all know we dont add certain things while with others we do.

A non sensationalistic introduction would have read more like, "Addition In Physics" or something.

But there are still interesting facts in that video things we dont think about every day.

An interesting real-world example of the case where 2 + 2 != 4 arises from the algebras of floating point formats.

Code:
#include "math.h"
#include "stdio.h"

typedef double real;

int main(int argc, char** argv) {
real two = pow(sqrt(2), 2);
real computed = two + two;
real actual = 4;
printf("computed: %g\n", computed);
printf("actual:   %g\n", actual);
printf("computed == actual: %s\n", computed == actual ? "TRUE" : "FALSE");
}
Output:

computed: 4
actual: 4
computed == actual: FALSE

#### nsaspook

Joined Aug 27, 2009
10,895
Of course one has to agree with most of that if not all, and it is an interesting video on how we add different things. I just dont like the way it is presented as it sort of borders on a sensationalistic grab line like we might see on the cover of a tabloid or a Huffington Post lead in advertisement or actually many lead in advertisements we see for what are really just a little education usually mixed with lots of advertisements.

For example:
"Guess what this guy did to this giant redwood tree with his bare hand..."
"You would not believe what scientists found in this pile of dung..."
"2+2=5..."

2+2=5 is just a little bit misleading because it suggests we have already accepted the premise that we are doing regular old grade school addition when really that is not the case. So during parts of the video i almost felt the need to say, "No kidding" We all know we dont add certain things while with others we do.

A non sensationalistic introduction would have read more like, "Addition In Physics" or something.

But there are still interesting facts in that video things we dont think about every day.
You want clicks, you need click-bait introductions on Youtube. The target audience is not you, it's people that might find this interesting and want to investigate further.

#### Deleted member 115935

Joined Dec 31, 1969
0
Do we know if there is some where a counter video to the OP one ?

#### nsaspook

Joined Aug 27, 2009
10,895

#### MrAl

Joined Jun 17, 2014
9,761
You want clicks, you need click-bait introductions on Youtube. The target audience is not you, it's people that might find this interesting and want to investigate further.
Well that's one view. Yes click bait i understand that all too well. The downside is that for 25 lines on a web page all with 'click bait' we cant be sure which of those we are really interested in until after we click it and wait for the page to load and read just a few more words so we know what they are writing about. That really bugs me because this happens to me all the time. I get these one-liners that are only partly descriptive and so i end up having to click a lot of stuff to be sure i am not missing something i really want to read about.
Let me throw out a few more examples...
Political News Now: "An important statement by the President says that..."
Physics News: "A new type of material that ..."
Science News: "We all would like to see one of the ..."

Now after reading those three for example, i may be interested in 0 of those or all three. But usually there are a lot more than that on one page that come up so i really find it annoying that i cant just go through the list and pick what i want to read right away, instead i have to click each one, wait, then read maybe three more words just to know if i want to read it or not.

For one example of what might come of that last one it could be something good:
"We all would like to see one of the new nano batteries become available to the general public and it will be coming to a store near you next month."
or something not at all interesting to me:
"We all would like to see one of the types of makeup available to clowns become safer to skin."

So that is the store of the evolution of 'click bait' for ya
Takes a lot of time to go through all the listings and maybe 10 percent are interesting to a given person.

I guess i could also say that i am a proponent of less creative poetic flair in science and more plain fact.

#### MrAl

Joined Jun 17, 2014
9,761
An interesting real-world example of the case where 2 + 2 != 4 arises from the algebras of floating point formats.

Code:
#include "math.h"
#include "stdio.h"

typedef double real;

int main(int argc, char** argv) {
real two = pow(sqrt(2), 2);
real computed = two + two;
real actual = 4;
printf("computed: %g\n", computed);
printf("actual:   %g\n", actual);
printf("computed == actual: %s\n", computed == actual ? "TRUE" : "FALSE");
}
Output:
Yes that is one that we always have to keep in mind when comparing results from floating point arithmetic.
So it can be even simpler than that:
2!=2
sometimes.
This is also interesting because sometimes it will print out in a console as "2" when really it is "1.9999999999999999" or something like that. Depends on the print format specifiers being used.
That is why it is good to use an algorithm to compare results.