Busy beaver by Ciro Santilli 37 Updated 2025-07-16
The busy beaver game consists in finding, for a given , the turing machine with states that writes the largest possible number of 1's on a tape initially filled with 0's. In other words, computing the busy beaver function for a given .
There are only finitely many Turing machines with states, so we are certain that there exists such a maximum. Computing the Busy beaver function for a given then comes down to solving the halting problem for every single machine with states.
Some variant definitions define it as the number of time steps taken by the machine instead. Wikipedia talks about their relationship, but no patience right now.
The Busy Beaver problem is cool because it puts the halting problem in a more precise numerical light, e.g.:
They are actually inheritable! But alleles are rare: www.ncbi.nlm.nih.gov/pmc/articles/PMC5559844
Figure 1.
To rats with the same genome differing only in DNA methylation with a different tail phenotype.
Source.
Spectral line by Ciro Santilli 37 Updated 2025-07-16
A single line in the emission spectrum.
So precise, so discrete, which makes no sense in classical mechanics!
Has been the leading motivation of the development of quantum mechanics, all the way from the:
Higgs boson by Ciro Santilli 37 Updated 2025-07-16
Initially there were mathematical reasons why people suspected that all boson needed to have 0 mass as is the case for photons a gluons, see Goldstone's theorem.
However, experiments showed that the W boson and the Z boson both has large non-zero masses.
So people started theorizing some hack that would fix up the equations, and they came up with the higgs mechanism.
Simons Foundation by Ciro Santilli 37 Updated 2025-07-16
Of all the rich person foundations, this is the one that feels the most hardcore.
They put huge focus on autism. Do they have an autistic child? Yes: www.forbes.com/pictures/eilm45mll/james-simons-autism/?sh=7825234250ce his daughter.

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