Monthly Archives: September 2012

Caturday’s Astronomy Pix for September 23-29, 2012


English: Computer simulation of the heating of...

English: Computer simulation of the heating of a space shuttle orbiter upon reentry. Temperatures on the exterior of the shuttle can reach during this phase of flight. (Photo credit: Wikipedia)

Equinox: The Sun from Solstice to Solstice

NGC 2736: The Pencil Nebula

Unusual Spheres on Mars

A Space Shuttle Over Los Angeles

Stars and Dust Across Corona Australis

Stars in a Dusty Sky

NGC 7023: The Iris Nebula

English: The Space Shuttle Atlantis atop the S...

English: The Space Shuttle Atlantis atop the Shuttle Carrier Aircraft (SCA) returns to the Kennedy Space Center after a ten month refurbishment. (Photo credit: Wikipedia)

Caturday’s Astronomy Pix is a weekly installment, published each weekend with links to each daily entry on NASA’s website Astronomy Picture of the Day. I hope you enjoy looking at these often breathtaking images as much as I do.

Fractal of the Week: Vermessika


Yes, I know that the title of this post is a silly neologism. But there are some nights when my faculty for made-up words needs to be sated.

This, though, is one of my favorites from the last few days, and needed something…different for me to call it. So take away my skeptic card and sue me.

I’d like to give a shoutout to my fractalizing friend Janet Russell at BuddhaKat, and offer my condolences of her losses on this date, and thanks for brightening my own evening with the images posted in her entry linked to below.

All images in this post are original works by the author, and are copyright 2012 Troy Loy

xkcd: Metallurgy


 

This work is licensed under a Creative Commons Attribution-NonCommercial 2.5 License.
This means you’re free to copy and share these comics (but not to sell them). More details.

 

How to Argue: A Sample Argument Evaluation


G’day. I’m foregoing the usual news item post for this updated completion to my earlier How to Argue post, in which I wrote on formally setting out arguments, and how we must analyze them, only evaluating them afterward to see whether the truth of the conclusion follows from the premises when an argument is either inductive or deductive in nature.

Here, we’ll evaluate an argument, and I want to use the argument I set out last time, and first going over the argument itself using a truth table to determine it’s validity as given. We’ll also note any insufficiencies of this argument immediately following, and how we can make it better.

Here it is as last time, in one row in formal notation. We are using sentential logic, or basic symbolic logic for simplicity…

P, Q, (P & Q)→R : R→S

And in English, the variables are repeated here from the previous post…

  • P – Expressions of belief are claims.
  • Q – No claim should get a free pass.
  • R – If you express your claims, but don’t like criticism, then you have two choices.
  • S – Your choices are to make better claims or to defend your claims.

…where commas are used to separate the premises, a colon to separate the premises from the conclusion, the “&” sign to join premises “P” and “Q” together as sub-premises with “R” in a complex premise, and the “→” sign to designate hypothetical or “If/Then” conditional statements into the 3rd premise, “(P & Q)→R” and the complex conclusion, “R→S.”

Note first that the truth of “R” depends upon the truth of “P” and “Q” together, and that of “S” depends on that of “R.” Already you might suspect that this doesn’t look promising, but let’s work that out, using all four variables and the full argument to see all of the possible worlds that the argument could pertain to, all possible situations, to see if there are any of these in which the premises may be true and the conclusion false.

That would show it to be invalid.

From a filled in truth table, we need find only one row where this is the case, and as we shall see, a truth table’s number of rows, or possible situations, doubles for each variable after the first. This one will have 16 such rows beneath the header showing the guide-columns for the variables and the guide-columns for the argument itself.

Each row on the table shows a possible variation of the truth values of the premises and the conclusion.

For ease of reading the table, I’ll use binary notation, with “1” for true, and “0” for false for the truth values of the variables and their operator symbols.

Well, glancing at the table, we don’t have to look far to see, at row 2 marked in red, that there does exist a possible combination of values in which all of the premises are true and the conclusion false.

P Q R S P, Q, (P & Q) R, R S
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 1 1 0 0
1 1 0 1 1 1 1 1 1 0 0 0 1 1
1 1 0 0 1 1 1 1 1 0 0 0 1 0
1 0 1 1 1 0 1 0 0 1 1 1 1 1
1 0 1 0 1 0 1 0 0 1 1 1 0 0
1 0 0 1 1 0 1 0 0 1 0 0 1 1
1 0 0 0 1 0 1 0 0 1 0 0 1 0
0 1 1 1 0 1 0 0 1 1 1 1 1 1
0 1 1 0 0 1 0 0 1 1 1 1 0 0
0 1 0 1 0 1 0 0 1 1 0 0 1 1
0 1 0 0 0 1 0 0 1 1 0 0 1 0
0 0 1 1 0 0 0 0 0 1 1 1 1 1
0 0 1 0 0 0 0 0 0 1 1 1 0 0
0 0 0 1 0 0 0 0 0 1 0 0 1 1
0 0 0 0 0 0 0 0 0 1 0 0 1 0

Sadly, despite any merits at all of it, it’s not a good argument, because as good logic students will quickly notice, it’s not complete.

What’s up with this? What’s wrong with it?

First, the original conclusion, “R→S” is better as the premise “R→S,” followed by the premise “R”, and the conclusion “S,” and the argument in full as follows:

P, Q, (P & Q)→R, R→S, R: S

So, let’s look at the truth table with this argument now completed, and see if it’s any better, with the added columns marked in green…

P Q R S P, Q, (P & Q) R, R S, R: S
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 0 1 1 1 1 1 1 1 1 0 0 1 0
1 1 0 1 1 1 1 1 1 0 0 0 1 1 0 1
1 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0
1 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1
1 0 1 0 1 0 1 0 0 1 1 1 0 0 1 0
1 0 0 1 1 0 1 0 0 1 0 0 1 1 0 1
1 0 0 0 1 0 1 0 0 1 0 0 1 0 0 0
0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 1
0 1 1 0 0 1 0 0 1 1 1 1 0 0 1 0
0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 1
0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0
0 0 1 1 0 0 0 0 0 1 1 1 1 1 1 1
0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0
0 0 0 1 0 0 0 0 0 1 0 0 1 1 0 1
0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0

Much better.

This is a valid argument, though that’s no guarantee of the truth of the conclusion, only of the conclusion’s truth if the premises are likewise true. What’s important to logicians is the truth-preserving qualities of such arguments.

On this now-completed truth table, there exists no possible situation, no possible world in which both the premises’ truth and the conclusions falsehood occur, no small matter even by itself for anybody concerned with truth in whatever form it takes.

Fractals of the Midweek: Pareidolia Fest I


Pareidolia…The natural tendency for human beings to see meaningful patterns in random data — where no such patterns nor meaning actually exists — just by virtue of humans being what we are. We learn through noting and recognizing patterns. For example, it is advantageous for us to recognize faces, especially human ones. Sometimes we make false positives — picking out these faces in ambiguous visual stimuli….

…and we are are particularly likely to see them in the oddest places; clouds, tortillas, engravings on coins, product logos, in television static; and that’s just visual pareidolia.

There are other sorts as well, such as seemingly picking out snatches of speech from recordings played backward, or voices from random radio static, so-called electronic voice phenomenon, or EVP. Those would be audio pareidolia.

So it also is with art, and so here I present a set of images from my collection that have evoked in others and myself the seeing of faces, and other, stranger sorts of things, that can be seen in fractals as with any visual or other sensory medium…

All images in this post are original works by the author, and are copyright 2012 Troy Loy

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