Loading...
Profile image
By Political Calculations (Reporter)
Contributor profile | More stories
Story Views
Now:
Last Hour:
Last 24 Hours:
Total:

Almost Proven

% of readers think this story is Fact. Add your two cents.


The Collatz Conjecture starts with a deceptively simple proposition. Pick a positive whole number. If the number is odd, multiply it by 3 and then add one to the result. If the number is even, divide it by two instead. Then repeat the process, only stopping if you get the value 1 as your result.

In 1937, German mathematician Lothar Collatz hypothesized that for any natural number you might choose to start with, you will ultimately end up with the value one as your final result. In the following chart, we’ve shown the trajectory of results you would get for each starting whole number you might pick from one to fifteen, which are called orbits in mathematicalese, which shows some of the inherent complexity that lurks within the seemingly simple algorithm.

Visualization of Collatz' Conjecture for n = 1 to 15

The Collatz Conjecture, or Collatz Problem, is one of the most famous open propositions in math, because in all the time since it was first proposed, it has not yet been proven. Sure, it’s been demonstrated for the first quintillion natural numbers (those with 19 or fewer digits), but no one has been able to definitively prove it applies for every natural number that might ever be contemplated.

That’s why it was big news in the math world several weeks ago when Terence Tao published a paper and blog post to claim that he had almost proven the conjecture. Tao is something of a rock star among mathematicians, where his contribution to the particular problem of the Collatz Conjecture was to determine that the potential counterexamples of where it might be false are extremely rare.

Alas, that’s not to say he found such a counterexample, which would officially close the Collatz problem because it would have been demonstrated to not be true, nor is it the elusive proof that there are no such potential counterexamples, which would also close the books on the question of the conjecture’s validity.

Loading...

Regardless, Tao’s paper represents forward progress in resolving the question, which may provide a foundation for future work that does ultimately prove the conjecture.

Part of what makes the problem fascinating is that it does lead to very interesting structures when the resulting orbits are visualized. For instance, if you look at the orbits for n = 14 (light orange) and n = 15 (light gray) in our chart above, would you have ever expected them to ‘reflect’ off each other through their first eight iterations before syncing to degrade together at their ninth iteration? Or that n = 9 would produce the longest orbit, with the highest number of iterations before degrading to one, for the starting numbers we presented?

If you prefer factor trees, you could check out Jason Davies’ Collatz graph application. Or, if you visualize many more orbits, you might get a structure that looks suspiciously organic, as Alex Bellow illustrates in the following Numberphile video:

But before you get too excited, we would be remiss if we didn’t leave you with xkcd’s take on the Collatz Conjecture.

The Strong Collatz Conjecture states that this holds for any set of obsessively hand-applied rules.

A little Collatz goes a long way!



Source: https://politicalcalculations.blogspot.com/2019/10/almost-proven.html
Before It’s News® is a community of individuals who report on what’s going on around them, from all around the world.

Anyone can join.
Anyone can contribute.
Anyone can become informed about their world.

"United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.

Support BeforeitsNews by trying our natural health products! Join our affiliate program
Order by Phone at 888-809-8385 or online at
www.mitocopper.com


Get our Free Ebook, "Suppressed Health Secrets"  with  Natural Cures THEY don't want you to know!

APeX - Far superior to colloidal silver! Destroys Viruses, Bacteria, Pathogens with Oxygen plus Silver!

Supreme Fulvic - Nature's most important supplement! Vivid Dreams again!

Ultimate Curcumin - Natural pain relief, reduce inflammation and so much more.

MitoCopper - Bioavailable Copper destroys pathogens and gives you more energy. (See Blood Video)
Oxy Powder - Natural Colon Cleanser!  Cleans out toxic buildup with oxygen! 
Organic Hemp Extract (CBD) - Full Spectrum high CBD (3300mg) hemp extract eases stiff joints, relieves stress and more!
Nascent Iodine - Promotes detoxification, mental focus and thyroid health.
Smart Meter Cover -  Reduces Smart Meter radiation by 96%!  (See Video)


FINAL WARNING!  Diseases are EXPLODING!  Watch this Video about APeX and You'll THROW AWAY Your Colloidal Silver!  APeX destroys Viruses, Bacteria and other Pathogens with the power of Oxygen PLUS Silver!  Nobody else has a product like THIS!   See why the inventor hasn't been sick in 16 years and why you'll never hear about it on the FAKE NEWS!  Get some now and tell your friends about it too so we can reach more people!  


APeX Interview - Superior to Colloidal Silver from Lee Canady on Vimeo.


Learn about APeX Here and Get the 50 Page Report in PDF format.   Call us at 888-809-8385 to order by phone.



Report abuse
Loading...
    Loading...

    Comments

    Your Comments
    Question   Razz  Sad   Evil  Exclaim  Smile  Redface  Biggrin  Surprised  Eek   Confused   Cool  LOL   Mad   Twisted  Rolleyes   Wink  Idea  Arrow  Neutral  Cry   Mr. Green

    MOST RECENT
    Loading...
    Load more ...

    SignUp

    Login

    Newsletter

    Email this story
    Email this story

    If you really want to ban this commenter, please write down the reason:

    If you really want to disable all recommended stories, click on OK button. After that, you will be redirect to your options page.