# Category Archives: Uncategorized

## On the difference between illustration and representation

If we paint a rectangle on a (3D) sphere, then there is no way to illustrate this rectangle as a rectangle on a (2D) map of the sphere. It is simply impossible to reduce a representation accurately with an illustration over a dimensional reduction.

However, since every illustration of a representation in any n-dimensional space actually is a reduced representation of an illustration of the same representation in an n+1 dimension, this fact means that illustrations can’t illustrate a representation accurately (in a general sense).

It means that it is not possible to illustrate a representation accurately at all. Illustrations of representations simply can’t fuse with representations. because the two are orthogonal (ie, diametrically opposed).

The problem is that that there is nothing in the middle. We can assume something an logically deduce something, or go the other way around, but we can’t find the middle.

## Is there “a tree of life” or not?

The question whether there is “a tree of life” or not is tricky.  At first, it appears to concern whether one believe in evolution or not, but at a closer look, it actually concerns the fundament for thinking, that is classification.

The closer look reveals that those of us that believe in the theory of evolution have an insurmountable problem to describe it in the form of “a tree of life”. The problem is that in order to describe it in this form, we have to assume that classes either are real or not real, none of which can lead to an unambiguous “tree of life”. Assuming that they are real leads an ambiguity concerning which tree that is “the true tree”, because classes are then fundamentally ambiguous, whereas assuming that they are real leads to a paradoxical ambiguity concerning which tree is “the true tree”, because classes are then fundamentally paradoxically contradictory. It does thus not matter whether we assume that classes are real or not real, we none the less end up in an ambiguity (pure or paradoxical).

The only difference between these two orthogonal approaches to this problem is that assuming that classes are real is unscientific (ie, self-contradictory), whereas assuming that they aren’t real is scientific (ie, consistent). This difference means that only the latter can lead to understanding of mathematics, and thereby also of quantum mechanics. Unfortunately, quantum mechanics is incomprehensible (except mathematically).

Assuming that classes are real is instead the fundament for the approach we call “populism”. It is the rational variety of extremism (like racism). The devil does thus reside on the back (the comprehensible) side of rationality. It appears sensible for rational people that can’t keep cocks and carrots apart.

## On the fundamental problem whether classes are real or not

The fundamental problem for us talking animals (humans) is whether classes are real or our inventions (ie, realism or nominalism). Intuitively, they appear to be real, but Russell’s paradox reveals that they can’t be. So, they thus aren’t real. Ie, nominalism wins.

It means that we can’t find classes, but instead invent them. This, in turn, means that race biology is unscientific. Isn’t that a pleasing fact?

## On the difference between science and populism

Logic is all about assumptions and deductions. We have to assume something to be able to deduce something. Deductions are then logically “true” based on their assumptions. It means that logic is sensible only if the assumptions are sensible, ie, self-evident or undeniable.

The fundamental problem with this procedure is, however, that every assumption also is a possible deduction, since the process of assumption-deduction can go either from the specific to the generic or vice versa, and that since every deduction from sensible assumptions also is sensible (per definition) there are two orthogonal (diametrically opposed) entrances to logic, and thus two orthogonal logical systems. We can, for example assume 1a. that Aristotle is human and 1b. that humans are mortal, and then deduce that Aristotle is mortal, or 1b. that Aristotle was an idiot, and then deduce that humans are idiots. In the former we deduce that Aristotle is mortal from the assumption that humans are mortal, and in the latter we deduce that humans are idiots by assuming that Aristotle was an idiot. Both these deductions are logically “true”, but the latter appears insensible.

So, what’s the problem with the latter deduction? Well, it appears to reside in that the assumption that “Aristotle was an idiot” is insensible, but it actually doesn’t. Instead, it resides in that we can deduce something about something inside a group that share some trait, ie, go from the generic to the specific, but can’t deduce something about something in a group from a single member of that group, ie, go from the specific to the generic. It is simply insensible to deduce that the swede Karl is stupid by assuming that the swede Arne is stupid (although none the less logical).

These two entrances to logic is called science (the former) and populism (the latter). Populism is thus not illogical, but just insensible.