Yes, dear reader, it was bound to happen sometime, I guess!
I slept soundly, having gone up to the bedroom before my wife got sleepy, and the dogs came up to settle in with me, too. And I slept, and I dreamed, and it had to do with ceiling squares and integer factorization, but symbolically. And it did not give me a solution – but a possible avenue of investigation.
In the dream, I have started a service to help people, people trapped at various heights. The heights seem to correspond to that ceiling square tower I posted several weeks ago, and they relate to the value of m, a number to be factored.
Now I have started this business, in my dream, and in comes someone whose Mother is trapped at such and such a height, and I take the Series of Ceiling Roots associated with the ceiling square containing that height, and it takes the woman safely AND EXACTLY down to ground level, in discrete steps.
Wow. I have not had MIRIAM – Moving Ideas Rapidly Into Accepting Minds – give me an early morning mathematical inspiration in exactly this fashion before. But it was what woke me up this time – not my dogs’ potty needs or their desire for a Denta-Stix snack on which to munch. It was this vision.
I got up, and frankly, dear readers, all I have done so far is just enough to verify that this might be a good idea for further investigation into factorization. The Series of Ceiling Roots generated by the ceiling squares of my biggest twelve-digit product of two six-digit prime numbers on the table of values I have generated indeed seems to have values close to the product of the terms of the Series of Ceiling Roots of the prime factors. It’s not exact, but it’s close. It’s not necessarily a profound finding, but to use a metaphor I’ve used a great deal lately, it is a new tree up which to bark. That is, MIRIAM has given me more work to do on integer factorization, and she did it in the most attention-getting way possible for me:
I am especially interested in my dreams. And this one, although not very long or complicated, was a doozy.
Thank you, MIRIAM.