The doubling circuit
What does 1 2 4 8 7 5 mean?
Real arithmetic, legend on top
It is what you get when you keep doubling and add up the digits of each answer: 1, 2, 4, 8, then 16 (1 + 6 = 7), 32 (3 + 2 = 5), 64 (6 + 4 = 10, then 1), and the loop starts again. Vortex math calls it the doubling circuit and reads it as the path energy takes. In plain math it is the remainders of powers of 2 after dividing by 9, which repeat every six steps and can never be 3, 6 or 9.
- The six-step loop
- 3, 6 and 9
Why it loops
Six steps, then home
Adding up digits keeps the remainder after dividing by 9. That is the whole trick behind digit sums, and it works because 10 is one more than 9 (the proof is here). So the doubling circuit is really a list of remainders: 1, 2, 4, 8, 16, 32 leave 1, 2, 4, 8, 7, 5 after dividing by 9.
It closes after six steps because 64 is 63 + 1. Two doubled six times is 64, and 63 is a multiple of 9, so the sixth doubling brings you back to where you started. Mathematicians say 2 has order 6 modulo 9. Every later power of 2 is the same loop again.
3, 6 and 9 never appear because a power of 2 is never divisible by 3. Only multiples of 3 have digits that collapse to 3, 6 or 9. Start the machine at 3 instead and you get 3, 6, 3, 6 forever. Start at 9 and every answer collapses to 9. That split, six digits in one loop and three standing apart, is the picture at the center of vortex math.
Any starting number follows the same track. Start at 7 and doubling runs 7, 5, 1, 2, 4, 8: the same loop from a different door.
Backward
Halving runs it the other way: 1 5 7 8 4 2
Halve 1 and add the digits of each answer: 0.5 gives 5, 0.25 gives 7, 0.125 gives 8, 0.0625 gives 13 and then 4, 0.03125 gives 11 and then 2, and 0.015625 gives 19, 10 and then 1. The same six digits, in reverse.
The reason is that halving is the same as multiplying by 5 and moving the decimal point, and 2 × 5 = 10, which is one more than 9. So times 5 undoes times 2 once digits are summed. Switch the machine to halving to watch it.
In the vortex diagram the six digits also sit in mirror pairs across the line through 9: 1 faces 8, 2 faces 7 and 4 faces 5, and each pair adds to 9. That is a property of the circle of nine, where a number and 9 minus that number always sit opposite each other.
What vortex math says it means
The doubling circuit, in its proponents’ words
Marko Rodin, who built vortex math around this loop, treats it as more than arithmetic. His own 2010 paper, written with Greg Volk, calls the doubling and halving paths “the most important feature of the Rodin map” and says: “Marko Rodin postulates that matter and energy naturally flow along these paths.” The same paper gives doubling and halving as “the patterns 124875 and 578421.”
This pattern perfectly demonstrates the way energy flows. Our base-ten decimal system is not man made, rather it is created by this flow of energy.Introduction to Vortex Based Math, a fan site, 2010
The same site calls the loop “a doubling circuit for a very efficient electrical coil,” which is the idea behind the Rodin coil. Rodin also calls it “the longest free-flowing path of the electron,” according to the Natural Philosophy Wiki.
None of this has been shown. The loop is a fact about remainders after dividing by 9, and that depends on counting in tens. In base 12 the same doubling visits ten digits, and in base 16 only four. Rodin’s paper itself says “no scientifically disciplined, quantitative, controlled studies have been published” on the coil. Nothing in Tesla’s writings mentions the loop either: his 1919 autobiography never uses the words vortex or doubling, and Rodin’s paper never names Tesla. Is vortex math real? goes through the rest.
Real vs legend
1 2 4 8 7 5, sorted
| Claim | Status |
|---|---|
| Doubling and adding digits runs 1, 2, 4, 8, 7, 5 and repeats. | Real · Powers of 2 mod 9 |
| 3, 6 and 9 never appear in the loop. | Real · 2 is not a multiple of 3 |
| Halving runs it backward, 1, 5, 7, 8, 4, 2. | Real · 2 × 5 = 10 |
| The loop is the same in every number system. | No · base 10 only |
| Matter and energy flow along this path. | No evidence |
| Tesla discovered or used the pattern. | No source |
Questions
1 2 4 8 7 5
What does 124875 mean?
It is the doubling circuit of vortex math. Double 1 again and again (1, 2, 4, 8, 16, 32, 64) and add up the digits of each answer until one digit is left, and you get 1, 2, 4, 8, 7, 5, then 1 again. Mathematically these are the remainders of powers of 2 after dividing by 9.
What is the doubling circuit in vortex math?
It is the loop 1, 2, 4, 8, 7, 5 drawn on a circle of the numbers 1 to 9, which makes a shape like an infinity sign. Marko Rodin’s 2010 paper calls the doubling and halving paths the most important feature of his number map and says matter and energy flow along them. That claim has never been tested.
Why don’t 3, 6 and 9 appear in 1 2 4 8 7 5?
Because only multiples of 3 have digits that collapse to 3, 6 or 9, and no power of 2 is a multiple of 3. If you start doubling from 3 you get 3, 6, 3, 6 instead, and from 9 you stay on 9.
What is 1 5 7 8 4 2?
It is the same loop run backward, by halving. 0.5 gives 5, 0.25 gives 7, 0.125 gives 8, 0.0625 gives 13 and then 4, and 0.03125 gives 11 and then 2. Halving works like multiplying by 5, and 2 × 5 = 10 is one more than 9.
Does 1 2 4 8 7 5 work in other number bases?
No. The loop depends on counting in tens. In base 12 doubling visits ten digits before repeating, in base 16 only four (1, 2, 4, 8), and in base 8 only three (1, 2, 4).
Is 124875 connected to Tesla?
Not in any source. Tesla’s autobiography never mentions doubling or digit sums, and Marko Rodin’s 2010 paper, the main written account of the pattern, never names Tesla. The link is a modern internet association.
Sources
Where this comes from
- Marko Rodin and Greg Volk, “The Rodin Number Map and Rodin Coil,” Proceedings of the NPA, vol. 6, no. 2, 2010: rexresearch.com.
- “Introduction to Vortex Based Math,” fan site with no official link to Rodin, November 30, 2010: archived copy.
- Marko Rodin, Natural Philosophy Wiki: wiki.naturalphilosophy.org.
- Primitive root modulo n, table of primitive roots (2 and 5 for n = 9): Wikipedia.
- Mark C. Chu-Carroll, “Numeric Pareidolia and Vortex Math,” Good Math, 2012: goodmath.org.
- Professor Puzzler, “Vortex Based Math with other bases and multipliers”: theproblemsite.com.
- Nikola Tesla, “My Inventions,” 1919: Wikisource.
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An image of the loop you traced. Copy link reopens it at the same step.
Poster
1 2 4 8 7 5 on the circle of nine, printed and framed.