Metabolic Rate and its connection with Surface Area
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Self-similar figures (such as fractals) primarily exhibit scale symmetry
Self-similar figures (such as fractals) primarily exhibit scale symmetry ((also called dilation symmetry or scaling symmetry), which is a type of similarity symmetry. Here’s a detailed elaboration: --- 1. What scale symmetry means In scale symmetry, an object looks the same (or statistically the same) when magnified or shrunk by certain factors. Mathematically, if you scale the figure by a factor \( r \), the result is congruent or similar to the original — but unlike translational or rotational symmetry, the “copy” is a different size. --- 2. Discrete vs. continuous scale symmetry - **Discrete scale symmetry**: Invariant under scaling by specific factors only (e.g., the Sierpiński triangle is invariant under scaling by factor \( \frac{1}{2} \), meaning if you zoom in by factor 2 on certain points, you see the same pattern). - Continuous scale symmetry: Invariant under scaling by any factor (e.g., a perfect straight line or a logarithmic s...
Commentary on the DNA Molecule
1. There is no way that the DNA molecule can be formed without a program, meaning, a programmer must be behind it. 2. The C value paradox evaporates if one views DNA under the lens of aesthetics. With less than 1% of the human genome intelligibly coding for function, we need to overthrow it. Period. It is clear that DNA is far from being a functional molecule. It is better to view DNA as an aesthetic phenomenon with functional elements thrown in to make it work. A change in perspectives is crucial but with funding and livelihoods at stake, such a perspective wouldn't be entertained. The view that the DNA molecule and everything else in nature is due to aesthetics just isn't popular, even though semiotics tells us so. I don't want to be to explicit but my implication is clear enough. The existence of fractals and fractal-like structures point invariably to an obsession with beauty behind the cosmos.
