Have you heard of the Collatz Conjecture?
This is so cool, I think this will totally blow your mind, at least it did for me.
I was reminded of this recently in my latest interview with Bo Polny.
For years, Bo has been coming on my show talking about the 4-2-1 cycle that he discovered and how it seems to play out over and over again in our world, whether that be on the grand scale of human history in terms of 4,000, 2,000 and 1,000 year periods, or whether that be in stock market and crypto cycles, or in countless other ways!
So I’ve heard Bo talk about the 4-2-1 cycle for a long time and then about a year ago a video suddenly popped up on my YouTube feed talking about the 4-2-1 puzzle in mathematics, often called the Collatz Conjecture or the 3x + 1 cycle.
Stick with me….even if your eyes glaze over the minute you see something involving math, I guarantee you’re going to like this.
So I clicked into the video and was stunned when it started explaining the Collatz Conjecture and how for centuries this has stumped mathematicians. The brightest of the bright have never been able to “solve” it.
Ok Noah, so what is it???
Glad you asked!
It’s really simple, and I basically think of it like a game. There are only two rules to the game and it goes like this:
The rule (also called the 3n + 1 problem)
Take any positive integer n.
If n is even, divide it by 2:
n→n/2
If n is odd, multiply it by 3 and add 1:
n→3n+1
Then repeat the process with the new number.
The conjecture
No matter which positive integer you start with, the sequence will eventually reach 1.
Once it reaches 1, it enters the repeating cycle:
1→4→2→1
This claim has never been proven for all positive integers, nor has a counterexample ever been found.
Ok so in layman’s terms, you can pick any number you want to start, but it has to be a positive whole number. No negative numbers and no fractions or decimals.
Simple example
Start with 6:
6 → 3 (even)
3 → 10 (odd)
10 → 5 (even)
5 → 16 (odd)
16 → 8 → 4 → 2 → 1
It reaches 1.
And then it continuously cycles in a never ending 4 → 2 → 1→ 4 → 2 → 1 cycle.
Another example
Start with 27 (a famous case):
The sequence climbs as high as 9,232
Takes 111 steps
Still eventually reaches 1
This is where it gets fun, testing it out yourself.
Go ahead and take any number you want (I really recommend NOT using 27) and test it out yourself.
Or feed it into an AI Chatbot and let it do the work for you.
Since we like the number 17 around here, let’s do that one:
Starting with 17, applying Collatz step-by-step until it reaches the repeating 1 → 4 → 2 → 1 loop:
17 (odd) → 3×17+1=52
52 (even) → 52/2=26
26 (even) → 26/2=13
13 (odd) → 3×13+1=40
40 (even) → 40/2=20
20 (even) → 20/2=10
10 (even) → 10/2=5
5 (odd) → 3×5+1=16
16 (even) → 16/2=8
8 (even) → 8/2=4
4 (even) → 4/2=2
2 (even) → 2/2=1
Once at 1, it enters the cycle:
1 (odd) → 3×1+1=4
4 (even) → 4/2=2
2 (even) → 2/2=1
So the full path from 17 down to 1 is:
17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1, then cycles 1 → 4 → 2 → 1 → …
I told you…really cool stuff!
If you want more, I discussed it with Bo a couple days ago right here.
Please enjoy:
Bo Polny’s website (Newsletter Signup): https://www.gold2020forecast.com
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Backup here on Rumble if needed:
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use code WLT49 (LIMITED TIME DISCOUNT)
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Oh and if you want to get a copy of Bo’s book, it’s beautiful!
Order direct on Bo’s website and get a 20% discount here:
Or grab it on Amazon if you prefer (finally back in stock, the new and updated Jubilee Edition):
With Silver over $80 as I write this article, one of the questions that came up on the interview from someone watching was: “Is now still a good time to buy silver?”
We answered that on the show and I would encourage you to watch Bo’s response!
But if you don’t have any gold and silver yet — or don’t have ENOUGH gold and silver yet — I have TWO great options for you.
And one can get you gold for no money out of pocket!
How do you like that?
BOOM!
First, you may recognize Andy Schectman from Miles Franklin.
He’s prolific on YouTube and just a brilliant guy, I’ve followed him for years.
I’ve partnered up with Andy’s company, Miles Franklin, and I’m really excited to show you what they can do!
In fact, Andy’s going to be coming on my show, the Daily Truth Report (follow us on YouTube and Rumble) in the future, and you’re going to want to make sure you don’t miss those.
Andy is a wealth of knowledge about the precious metals markets and crypto, and I’ve covered him here many times in the past.
Now I’ll get to chat with him myself, and I’m really looking forward to it.
I’m spoken directly with Andy and his team and they have assured me they will take very good care of anyone in the WLT Report family (that’s you!).
At Miles Franklin, everyone gets personal attention from their team of brokers and you’ll get whatever level of hand-holding you prefer. They’ll also customize a deal just for you, but you have to call them and tell them NOAH sent you! They’ll handle it from there. 1-952-929-7006
There is no minimum order size and no maximum limit.
I think you’ll love working with them, I already do!
You can reach them at 1-952-929-7006 and make sure you let them know that Noah sent you over, they’ve promised me the best of the best service and pricing for everyone in the WLT Report family.
Second option is a company I’ve talked about many times before, it’s Genesis Gold.
I’ve worked with Genesis Gold for three years now, and they are excellent at what they do.
Genesis Gold is for people who want to purchase real physical gold or silver in their IRAs (Investment Retirement Accounts).
You know what the beauty of that is?
Two huge benefits actually…
One is that it’s TAX FREE baby!
I’m not a tax advisor, but that’s a general oversimplification.
Never pay more taxes than you are legally required to pay.
And that’s why I love getting gold and silver in my IRA (and why I hold a large chunk in an IRA myself!).
The other is if you simply shift money out of stocks (like Peter Schiff recommends) and into Gold, it won’t cost you anything! No money out of pocket!
BOOM!
There’s so much to love about Genesis Gold, starting with the fact they are proudly and un-ashamedly Christina!
They call it “Faith-Driven Stewardship” and they put it right on the homepage of their website along with a quote from Ezekiel:
Wealth Preservation With Gold & Silver –
The Genesis Gold IRABy your wisdom and your understanding you have made wealth for yourself, and have gathered Gold and Silver into your treasuries – EZEKIEL 28:4
Genesis Gold Group believes the Bible gives clues on how man-made currencies (paper money) represent instability, and a lack of virtue and encourages living wastefully in excess.
Conflicts have beleaguered us since the dawn of civilization, and they can all be encapsulated into one battle. The battle is between currency, man-made paper, and gold and silver — the two precious metals found in our Earth’s crust, sent to us by our Lord to use as money. Man-made currency always leads nations down the path to increased war, greed, and ultimate collapse. History has shown that abandoning gold and silver has always been a bad idea. Gold and Silver enforce discipline, nurture self-constraint, self-reliance, and balance, and lead to confidence, a restrained government, and a more stable foreign policy.
Genesis Gold Group believes in empowering faith-driven stewardship with Gold & Silver are an integral part of a balanced portfolio. Protecting your finances with precious metals has never been more crucial during these trying times.
With a combined 50-plus years in the precious metals industry, let your Genesis gold and silver experts guide you through the simplicity of asset protection and growth with our Genesis Gold IRA.
Sincerely,
Empowering Faith-Driven Stewardship
Oh….and they’re VERY good at what they do.
You also get physical gold and silver with Genesis, believe it or not! The gold and silver is purchased for you (in whatever combination of coins and bars you prefer, a picture taken and sent to you, and then stored safely in a vault for you!
I love what these guys are doing.
Here’s more on why gold and silver in your IRA are so powerful:
You can contact Genesis Gold here.
They are also very backed up with record demand, so you may have to wait a bit, but someone WILL get in touch with you for personal customer service and assistance!
Tell ’em Noah sent ya!
Oh, and did you know Genesis is recommended by SUPERMAN himself?
It’s true.
Superman himself, Clark Kent — Dean Cain — came on my show a few weeks ago and we broke it all down:
Watch here:
Stay safe!
This is a Guest Post from our friends over at WLTReport. View the original article here.
