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  • The Horizontal Paradox
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    • Home
    • 12 steps to T-Shirt Logic
    • Imaginometry
    • Evidence Room
    • Level is horizontal Test
    • Illogical arguments
    • T Shirt Logic
    • The E.A.o.A
    • Realising Euclid
    • The Horizontal Paradox
    • Tis '''globe'''
    • Advanced Simplicity
    • Rumpus Pole
    • The Real '''globe'''
    • Terms
  • Home
  • 12 steps to T-Shirt Logic
  • Imaginometry
  • Evidence Room
  • Level is horizontal Test
  • Illogical arguments
  • T Shirt Logic
  • The E.A.o.A
  • Realising Euclid
  • The Horizontal Paradox
  • Tis '''globe'''
  • Advanced Simplicity
  • Rumpus Pole
  • The Real '''globe'''
  • Terms
On The Level

Welcome to the home of Levelology, we seek a balance and understanding.

Welcome to the home of Levelology, we seek a balance and understanding.Welcome to the home of Levelology, we seek a balance and understanding.Welcome to the home of Levelology, we seek a balance and understanding.Welcome to the home of Levelology, we seek a balance and understanding.
Do you question the little things you take for granted?

Find Reality and Start to Lose the Model

The next twelve steps may cause you to reconsider the reality you've been given, you may find the perception of what you think you know to be at odds with what you've been taught. There's hidden depths within what we call 'Advanced Simplicity'

Some of these facts may cause you pain, please read the warning below.

Cognitive Dissonance

Welcome

 Cognitive dissonance is a term for the state of discomfort felt when two or more modes of thought contradict each other. 

Cognitive Dissonance
Straight lines don't bend or curve

Straight line is Right

A RIGHT line is that which lies evenly between its extreme points, that is without curvature in any direction being  the shortest path between those 2 points, never deviating from that path.


This is not a concept but a fact of reality and basic logic.

Straight explained
Euclid's Elements Book 1 Definition 5

The Plane (superficies)

A superficies (plane surface) is that which has ONLY length and breadth

Those two dimensions - Length and breadth make this a 2D conceptual surface on which Plane geometry is based.

This 2D plane obviously does not enter into 3rd dimension.

Plane resource
Euclid's Elements Book 1 Definition 10

Perpendicular

When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called perpendicular to it.


As stated in Axiom 11, all right angles are equal therefore the lines must be STRAIGHT 

Perpendicular
Euclid's Elements Book 11 Definition 3

Perpendicular to a Plane

A straight line is perpendicular, or at right angles, to a plane, when it makes right angles with every straight line meeting it in that plane. 

Book 11 Proposition 6 states; if two straight lines be at right angles to the same plane then they shall be parallel to one another.

Perpendicles ftw
Let's get real

Vertical

At right angles to the horizon; perpendicular; upright. 

In mathematics it is a plane, position or straight line.

Perpendicles ftw
Not just a straight line

Horizontal Plane

Parallel to or in the plane of the horizon. 

At right angles to a vertical line.

In mathematics either measured or contained in a plane parallel to the plane of the horizon.

Horizontal
Cartesian axis

Horizontal and Vertical

Horizontal and Vertical geometrically are perpendicular, with Horizontal being the plane and vertical being perpendicular to it.

They both have a common factor being the horizon, which they are either parallel or perpendicular to. 

Perpendicular
Cartesian axis x,y,z

Reference frames Horizontal and Vertical

In reality horizontal and vertical are the reference frames we use as our baseline, any inclined plane will be measured as an angle to one of these reference frames.

Perpendicular
Perpendicle

Plumb Bobs and Perpendicles

A perpendicle is ANY thing hanging down by a strait line.


A Plumb Bob is a tool for establishing a vertical reference, this is used in reality daily by many people.


A vertical line is a straight line.

The right angle
Level is a right line on a horizontal plane

Level

Level is a straight line on a horizontal plane.

A level is a tool for establishing a horizontal plane of reference from which vertical distances can be measured.

An instrument for determining whether a surface is evenly horizontal.

From Latin libella "a balance, level".

Level is horizontal
Perpendicularity

Its all right

The relationship between reality and geometry becomes apparent with the right line relationship between the 2 frames of reference used in everyday life. 


Level and Plumb are perpendicular.


Vertical and horizontal are perpendicular.


This is NOT a coincidence - Geometry is reality.

3 4 5 triangles
Here's the reality link again

Water level (tool)

A water level is any device utilising the surface of liquid water to establish a horizontal plane of reference. 

The water level is lower tech than the more modern levels, but it can be more accurate over long distances, and works without a sightline, such as around corners.


2 ends = 2 points at an even altitude.

Level is horizontal
Euclid's Elements Book 1 Proposition 30.

T-Shirt Logic

All horizontal planes are parallel.

 Book 1, Proposition 30.

Straight lines which are parallel to the same straight line are parallel to each other.

Book 11, Proposition 9

2 right lines which are parallel to each other.....

Once again the link between reality and geometry becomes clear, you already know it to be true.

T-Shirt Logic
Where's the cog dis?

How will you react?

How would you react if you were told that you'd probably want to change one or more of the above statements, once reminded of a model, you've never been taught anything about, and only ever imagined as being real?

This is NOT a trick, but it does expose the trick that has already been implanted in your imagination.

Do you imagine your geometry

Copyright © 2025 On The Level - All Rights Reserved.

  • 12 steps to T-Shirt Logic
  • Evidence Room
  • Logic and philopsophy
  • Illogical arguments
  • Oakley's law

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