Recent content by phyti

A measurable change in dimension in the direction of motion vs. an apparent visual image change. Here is another example specific to the MMX.

alexandrinushka; A metal rod can be measured, heated, and measured again, revealing a change in dimension, all occurring in a single ref. frame. Materials can be transformed via various processes, thus there are no 'rigid' objects. Changes in dimension and composition are a common part of...

jbriggs; Things were looking good up to the red statement. Always searching for simplicity, here is another graphic. The sequences remain defined as before and 12 are randomly selected and identified with a line number. Make a copy of a randomly selected sequence from the sample, say 9, and...

forum; Thanks for the Q&A session. It was valuable constructive criticism. As the author, you can't know if the reader interprets the contents as intended. Feedback is needed to correct errors, clarify, simplify, add detail, etc. In Cantor's diagonal argument, the difference in interpretation...

forum; part 3 comments to me: "One sense in which it is inequivalent is that a completed infinite binary tree has no second row." This is an abstract 'tree' showing connectivity of its elements according to some form of order. It has no leaves and bears no fruit. L begins in position 0 with...

forum; part 2 translation of Cantor's diagonal argument: From the proposition proved in § 2 there follows another, that e.g. the totality (Gesamtheit) of all real numbers of an arbitrary interval (a ... b) cannot be arranged in the series w1 w2, …, wv, … However, there is a proof of this...

forum; part 1 The set N of natural (counting) numbers enables an ordering by size (cardinality) of finite sets. Cantor's concept is a set of transfinite numbers that enable a similar ordering by size of infinite sets. He sees this as an extension of the number system, and considers a...

BWV; p and d are from the pdf example. The graphic shows how p, the sequence formed from the diagonal d is actually an element of L, yet goes undetected. Sequence d is a simple alternating symbol beginning with 0. The complement p is therefore an alternating symbol beginning with 1. The...

If the sequences are not ordered by any specified pattern, then they are random. Cantor, nor anyone else can show you a complete infinite list. It's an abstraction that cannot be made manifest for viewing. The ellipsis (...) is supposed to inform you that the data extends without limit.

The citation is for people who may not be familiar with the subject. A second source is http://uk.geocities.com/frege@btinternet.com/index.htm Copyright © E.D.Buckner 2005, a translation of Cantor's 1891 paper. Here is a counter example showing probability doesn't constitute a proof...

forum;, By persevering on and off for some years, we can now slay the 'diagonal dragon'.

With a more accurate drawing, more visual clues may stand out. Angles are multiples of 10. Connected lines from CB perpendicular to AB or from AB perpendicular to CB can only form (20,70) right triangles. In lower image, form EF and EG. If a 70° line from G meets a 90° line from D at the same...

I agree with simplicity. Was just making calculations for doppler effects, and thought this would work, but needed another opinion. Thanks.

I don't remember seeing this solution to the question. Imagine an object of length d with a reflector on the far end (x=4). A moves past the object at speed a, emitting a signal at the origin in the positive x direction. A makes one pass in the +x direction, reverses and makes one pass in the...

NoahsArk; Since light serves as a universal measurement tool, the light clock is a logical place to start for understanding of Special Relativity. Experimental evidence has shown the propagation speed of light in space (vacuum) is constant and (more importantly) independent of its source. The...