• [deleted]

This may seem too simplistic but the minimum path issue, could we use the bread crumb principle. Spread virtual bread crumbs and just sort out the paths by counting the least crumbs?

I am not a scientist or mathematician so feel free to ignore me.

Use a graph to sort out the numbers and as you get more data calculated you would (my guess) be able to eliminate the ones that probably will fall outside your goal.

my email is eightbitme@gmaail.com

or no1athomedotgov@outlook.com

or even sdc15485863@yahoo.com

(say that number looks familiar what is that number)

Hint it is a prime # but what one?

10 days later

Still the thought nags.

Is not Occum's Razor--be it Kolmogorov complexity/(Chaitin's) algorithmic information--merely the approximation of a rapidly decaying tail of an infinite distribution of possibilities.

In the greater scheme of things, will assuming such a decaying tail still prove valid?

14 days later

"whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure."

The question how large is the sum 1/2 1/4 1/8 ... can be quickly and plausibly answered by means of common sense but definitely not by direct procedure.

While Kolgomorov's idea is convincing to me, I did not yet grasp its promised application.

Let me reiterate a seemingly quite different statement of mine: Addition of redundancy, in particular with complex valued Fourier transformation (FT) instead of equivalent real-valued cosine transformation (CT), can effectively be considered as causing incompleteness if the original mathematical model pf concern resides in R* instead of R. In terms of physics: Future data cannot be measured in advance.

CT is then not just simpler than FT but also basic to it. Can you imagine a physics that needs ict and ih_bar merely for the sake of convenience and tradition?

Eckard Blumschein

5 days later
  • [deleted]

First, Occam's Razor is very likely a kind of least energy principle. That is, it suggests the least energy solution to a problem, viz., that the best solution to a problem creates the fewest new terms, hypotheses, etc., in explaining a phenomenon. In this case, it's thermodynamically efficient when compared to the other hypotheses which purport to explain a phenomenon. It's a process comparing the energy cost outcomes of the other hypotheses.

But what does it mean to "explain"? That is the problem here in a nutshell. What, for that matter does "understand" mean in neurophysiological/mental terms? If we look at the model of evolution, we see this in action. Evolution states simply that all life comes from previously existing life, by means of variations in the individuals of species, which transmit through genes those advantageous characteristics to their offspring. Acting through those individual characteristics, some of which are more efficient/effective than others, leads, by the compound interest rule of 72, an evolutionary advantage over generations, formerly called fitness, but now cast into a least energy, thermodynamics rule, instead. Evolution concepts are used because those widely and efficiently explain how the species developed, in the same, analogous way that Newton's laws of motion explained efficiently the basics of mass, momenta, and energy. The relationship to creativity is at once apparent, too.

The best explanation is therefore energy efficiency compared to other possible explanations. We get a lot of good explanations from the idea of evolution compared to others.

Interestingly enough, recognition also has a characteristic that it's efficient, when compared to other possible recognitions. It's Least Energy Principle in many cases, too. It explains/comprehends the event which is to be recognized using least energy to do so.

This point should be taken into consideration when trying to quantify and understand Occam's Razor.

Feynman's diagrams and how they drastically saved time in figuring particle interactions compared to Schwinger's exhaustive calculations, are also the least energy rule.

Regarding category mathematics, hierarchies and categories create problems for mathematics, but not if using verbal thinking, is also the case.

How protons/electrons give rise to atoms, which give rise to compounds for instance, or carbon atoms' bonding gives rise to polymers, protein chains and those to enzymes, the latter an even higher category, as well. Tough for math to scale up, but easy using language.

Write a Reply...