Nope that’s not a typo and this isn’t technically about religion. This post is about holes in space, namely black holes, wormholes, and the lesser known white holes, and their implications to the physical and metaphysical. The arrangement or flow of exposition of this article, from black to worm to white hole, will become much clearer as you read along the article. So get ready for a quick rundown on holes (cosmic ones of course), thought experiments, sci-fi love, paradoxes, and various possible implications in our lives and the universe we live in.

Artist's conception of a back hole

Black holes

The scientific definition for  black hole, specifically in general relativity, that I prefer is that it is a region in space whose escape velocity within its event horizon exceeds the speed of light, and at its core is a singularity. What this means in more layman’s terms is that a black hole’s gravitational pull is so massive, which gives the more well known fact that not even light can escape it.  The reason is that, for an object to escape or “pull out” from a celestial body, whether this be a planet or moon or sun or in this case a black hole, the object must exceed the body’s escape velocity. On Earth, rockets launched into space must have an escape velocity that exceeds 11.2 Km/s, which is the Earth’s escape velocity. For black holes, the escape velocity is greater than 300,000,000 m/s (speed of light). Since we know of nothing that can exceed the speed of light, light and everything else therefore can’t escape the black hole.

You can actually think of a black hole as having sections, very much like a planet’s interior or even an avocado. The event horizon of a black hole is a sphere surrounding the black hole, and is the point of no return. Once you fall into the event horizon, there’s no going back.

The next section is the singularity. Singularity is a fancy term in physics and mathematics which means infinite density or infinite curvature. Density as you recall is mass divided by volume. When an object, which has mass, is compressed to zero i.e. a point with no dimension or volume, then you get a singularity. You could think of a black hole as “pinch” in the fabric of space-time which I discussed in an earlier post of mine. You can also think of it as a vortex, similar to a whirlpool when you stir water in a glass of water and you create a funnel-like shape. In this case, it’s a vortex in the space-time continuum, which could possibly lead to alternate universes.

One of the more curious and famous implications of black holes, and further down the road for the other cosmic holes, is time travel.

Physical/Metaphysical implications:

The famous physicist Stephen Hawking jokingly conjectured, “If time travel is possible, then where are the tourists from the future?”. Of course a lot of silly and smart alec answers can be given, but if you really think about it, it’s a genuinely profound question. If time travel was indeed possible, what of history? People could go back in time rewriting history as they see fit, or just altering some events in their lives whether trivial or not, and which could have disastrous consequences in the future.

In fact, if time travel is possible and there are/were time travelers among us, we could be living in an alternate universe where the 9/11 attack happened, and that the Dalai Lama was never killed. One alternate universe then had any of the combinations happen: 9/11 happened and the Dalai Lama was killed, 9/11 didn’t happen and the Dalai Lama wasn’t killed and so on. This possibility is under the many worlds interpretation, where there are countless universes, where every conceivable or even inconceivable outcomes occur.

The movie series Back to the Future does not use the many worlds interpretation however, since in this case if you change something in the past, you “erase” whatever that change could have been in the future. In other words, if you kill somebody in the past, then in the future, everyone who ever knew that somebody will immediately forget about him/her. Everybody related to that somebody, including events, will also be removed/erased out of existence and history, just like erasing your sketch on a piece of paper. This type of interpretation of the universe, although good for entertainment and sci-fi, has more paradoxes and questions left unanswered, that’s why I am more inclined to take on the side of the many worlds interpretation.

Another paradox of time travel is that you can be your own child, father, and mother.

Consider a brilliant man who who was raised as an orphan and invents things for a living. He eventually meets a mysterious woman and marries her, copulates with her, and they conceive a child. Sometime later the woman then mysteriously disappears along with your child. Distraught with grief, the man pours all his time and effort to building a time machine. Unfortunately, successfully building a time machine wasn’t enough to fill the emotional void for the man, and so he decides to have an operation and have his sex changed.  Furthermore, she (previously a he) decides to go back in time as an escape to it all. She then travels back in time, meets a brilliant young man, bears him a child, and then decides it was wrong to do so. So she takes the child with her into the time machine and leaves the child at a much earlier time in an orphanage.

These types of paradoxes can quite certainly make your head spin, while trying to unravel the tangle in the family tree. The man/woman/child was an entire family all by her/himself!

 

2D representation of a wormhole

Wormholes

Worm holes, although recently coined in 1957 by theoretical physicist John Wheeler, and theorized as early as 1921 by mathematician Hermann Weyl, have been part of popular fiction since the 19th century. By this I mean the wormhole in the famous (and one of my favorite books) children’s book Through the Looking-glass, and What Alice Found There by Carol Dodgson or more commonly known as Lewis Caroll. The looking-glass in this case is reminiscent of a wormhole, i.e. a pathway to another universe.

Much of what is written here relates to transversible wormholes, or wormholes that won’t destroy you or your starship as you travel through the hole, unlike other proposed wormholes which aren’t transversible by starship. Much of the transversible wormhole information started from famous physicist Kip Thorne and his colleagues.

The illustration above is a 2D analog of a 3D wormhole. In reality, a 3D wormhole is really on a 4D space-time. But usually 2D analogs make the concept much easier to visualize and grasp. In this illustration the shortest distance from one point in space to another is not a straight line, but instead, a wormhole. This is clearly seen when you have 2 points on a piece of paper. Naturally you’d think a straight line is indeed the shortest path between the points. However, if you fold the paper such that the 2 points are directly opposite of each other, then a direct path/link from one point to the other via this curved/folded arrangement is most certainly shorter than a straight line on the piece of paper. This is similar to the case of a wormhole. In the image above,  a light ray is represented by a single line.

Physical/Metaphysical implications:

One cool, currently hypothetical implication of wormholes is multiply connected space. Let’s do one thought experiment again shall we?

Imagine you’re in a museum staring at a painting by Picasso. Now you were suddenly startled by something appearing in front of you, so you momentarily move your attention away from the Picasso artwork. You find that there’s a mirror on the space in front of you. Or rather, a hole floating in the space just in front of you.

When you peer into the hole, you see your father when he was just 17! He then stares at you, not knowing you will become the future fruit of his loins. You become more curious (I know I would!) and decide to go around/behind the hole, to find out what you will then see there. Amazingly you don’t see your father or your father’s back, but instead you see your mother when she was 17! Again, she looks at you perplexed, thinking how oddly dressed you are.

You then realize that this is the prom night of your mother and father back in high school, in a different time and place. From your mother and father’s “universe” however, they were also startled to find a mirror or hole between them while they were dancing. When your father, 17 yeas of age, peers through the hole, he sees a strangely dressed young person looking surprised (you). From your mother’s POV she sees the Picasso painting. But since you decided to move around the hole to observe further, your father saw you leave the mirror. Your mother on the other hand sees a young person block the view of the Picasso painting.

But being the curious fellow that you are, you decided to look at the hole sideways, only to be surprised at the fact that you can’t see anything from a sideways POV, nothing even remotely as thin as paper. Is that cool or what?

Here’s another cool trick you can do at this point: Suppose you wanted to shake hands with your father, so you stick your arm into the hole (never minding the large gravitational forces or radiation that will crush your arm if this was a non-transversible wormhole). Your father reaches out a hand and shakes yours. However you notice that you can also stick your other arm into the other side of the hole, and so you do. You find out that you’re now shaking hands with your mother. Out of this world right?

White holes

White holes are reversed black holes, in that they spew out matter/material. As you may have already figured out, the complete picture of a “tunnel” through space-time ends with a white hole. That is, it usually starts with a black hole, which then creates a wormhole, and then exits via a white hole.

Physical/Metaphysical implications:

Recently some scientists, based on their research, proposes that white holes are actually starters of “Big bangs”, i.e. they create universes, and that the number of universes created by our own universe is directly proportional to the number of black holes in it. This is because, if the theory is proven correct, on the other side of a black hole is a white hole, wherein perhaps all the matter that fell into the black hole would come out in an immense fashion out through a white hole.

This could then mean that the theistic, common Judeo-Christian interpretation of God therefore didn’t create our universe, since at the very least there was a minimum of one universe from which our universe owes its existence to.

Resources, references, and further reading

• Wikipedia article on black holes
• Wikipedia article on wormholes
• Wikipedia article on white holes
• Wikipedia article on the many-worlds interpretation
• Through the Looking-Glass, and What Alice Found There, in different ebook and mobile formats, free for download.

• Hyperspace-A Scientific Odyssey Through Parallel Universes, Time Warps, and the Tenth Dimension, Michio Kaku, ISBN-0-385-47705-8

Mathematics is for everyone. Really.

This article ( and the succeeding ones in the series) aims to prove that point. That everyone has a mathematical brain. Specifically, I’ll concentrate on a certain area of mathematics in this article known as geometry, and then go to more advanced geometry (usually college or graduate level geometry). Don’t fret! There are no equations here which will make your eyes wander and do something else (at least while you’re reading the article). There are a lot of  science articles around, but what you usually don’t get often are articles about math, how beautiful and useful it is, and how important it is to science and modern civilization.

A Short Love Story

I love math. That’s how I feel about it: I’m passionate about it, just as I am a passionate about science (particularly physics), sci-fi (Star Trek et al) and technology (programming, software et al). However I started out disliking math in grade school. Like many things in my life which started with me disliking them but ended up with me liking them instead, my love for math grew more and more as I progressed through grade school, then through high school and then college. I disliked math at first because I didn’t pay much attention to studying it, and considered it far less important and impressive than science at that time. The effect then was that I performed poorly in math. As I paid more attention to math however, I learned I was quite skilled at it, and that it was fun for more than one reason. In short, as the years progressed and I learned and matured along with math, I fell in love  with it as well.

The Real Mathematical Deal

Unfortunately a lot of people (all over the world you’d be surprised, even in well-developed countries like the UK and the US) both young and old struggle with math. Oftentimes you’ll read/hear news about how kids from different countries around the globe, from grade school and so on, struggle with math.  They are usually victims of many unfortunate circumstances which I don’t think , mind you, include not having what is commonly labeled as a “mathematical brain”. Humbug. These circumstances I refer to include a poor/ineffective educational system, poorly trained/ineffective teachers, lack of support from people around you, or combinations of those. Those of us who turned out to love and appreciate math for its beauty, purpose, and elegance, are the fortunate few I think. The exceptions to the rule perhaps. But like I said, humbug. Everyone is born with a mathematical brain, it’s just that we don’t realize it most of the time.

Most of us think about long, boring, frustrating, confusing (and perhaps frightening sometimes?) equations when we think about math. Our grade school teachers made us memorize the multiplication table from 1 to 10 (I heard some even go as far as 15). In high school we learned algebra, or perhaps some of us didn’t, unfortunately. Perhaps some of you later on in life cursed (or still curse) the Arabs for improving  and making algebra very widely known and used.

The truth is, mathematics is a large collection of sub-areas of interest, and algebra is but one of them. Some,as you may already know, include geometry, trigonometry, discrete math, and so on. In this post, which is one among a series, I will show you that not only do you have a mathematical brain, but that you can grasp even advanced ideas, in this particular case, geometry. Now let’s get to it shall we?

Dimension hopping

Please observe the figure below (Figure 1), which includes objects (a) to (e). We first start out with an object with no dimension, which is a point in space (a).

Then, if you have two points,  connect them together and you have a 1 dimensional object, a line (b). In fact, if you recall your basic high school geometry, a line is just a series of points. The only dimension in this case is of course the dimension of length. So far so good?

Now, if you have a line (b), and then another one similar in length as well as parallel to it, connect their ends and you get a square (c). Now you have a 2 dimensional object, which has both the dimensions of length and width. See where this is going?

Next, if you have two squares which are of the same size, you connect their edges and you get a cube (d). Obviously this is a 3 dimensional object, having width, length, and height/depth.

Finally, and usually this is tackled in more advanced math/geometry courses in college, we extend the 8 corners of the cube and get what is known as a hypercube, in this case a 4 dimensional hypercube (e). You can also imagine this as a smaller cube within a larger cube, and then you connect their edges.

You’d notice that, in order to go to higher dimensions of cubes, you’d just keep on extending and connecting their edges/corners. Easy as pie no? And you just had a 101 on advanced geometry. Many people don’t know that math, especially in advanced courses, involves a lot of imagination and creative as well as abstract thinking. Cool no?

Figure 1: from 0 to 4 dimensions

Great, great. But what’s the use?

What’s the use you say, old chap? What’s the use of knowing how to create hypercubes? Why, quite a lot actually. Aside from the cool realization that you just used your imagination to waltz through an advanced math/geometry class, hypercubes such as the 4D one in the figure (e) have lots of uses.

One is aesthetic. As you can see in the figure below (Figure 2), the Grande Arche in Paris, France is quite a beauty, and one hell of a tourist attraction. It looks so futuristic to me too. It’s inspired by a 4D hypercube such as the one shown above in Figure 1 (e).

Figure 2: Grande Arche in Paris

Another is that hypercubes are used in supercomputing, or computing that involves trillions upon trillions of data. Supercomputing  is necessary and used in weather modeling and prediction, aircraft design, and other scientific and compute-intensive areas and applications. The interconnections of the computers are in 4 or more dimensional hypercubes.

And lots more. In fact, we may still discover more uses for hypercubes in the future. When hypercubes were first realized and imagined many many years ago, mathematicians didn’t really know what good they were for. It was just that it was their work to do math, they were curious, bored, or something in between. What they didn’t realize is that their work would pave for more wonders which our generation now enjoy and is rarely aware of.

So, still think math (or at least more than one area of knowledge in it) isn’t for you? Or that it’s hard to get into advanced math? If you don’t think so, or that you’ve slightly changed your  opinion about the topic (about math not being for everyone) then my article has somehow served its purpose. If not, then keep reading my future posts on how everyone can do, use, and even love math as I do. Perhaps even more.

Resources, references, and further reading

• Wikipedia page on hypercubes: http://en.wikipedia.org/wiki/Hypercube
• Wikipedia page on The Grande Arche: http://en.wikipedia.org/wiki/Grande_Arche
• Wikipedia page on the use of hypercubes in complex computing: http://en.wikipedia.org/wiki/MIMD

This article discusses why the colloquial expressions such as “That’s why I gravitate towards you”, “I’m falling for you”, and “She is attracted to me” can be quite scientifically accurate. The following article muddles up the meanings of casual words like “falling” and “attraction” with the currently accepted theories, studies, and findings of physics on the related matters. I’ve done something like this before , similar in fashion to how the word “God” is poetically and figuratively used in relation to the “religious”  views of Einstein, Stephen Hawking, and other physicists . This time, it’s love.

First we have Space-Time

Space-time or spacetime is a mathematical model that you get when you combine the 3 dimensions of space with a 4th one,  the dimension of time.  In a nutshell, space-time is similar to a landscape where a point locates an event i.e. a 3 dimensional location + the time when it happened, instead of just a usual, spacial point in space like in maps, even if it’s a 3D map. Since space-time involves 4 dimensions, even most scientists find it very hard to imagine what 4 dimensions would look like, since us humans are accustomed to only 3 dimensions of our space. We always look at time as something that is fixed and unchanging. Newton certainly did when he wrote the laws of motion. One of the most impressive feats of Einstein was that he showed this was not so, and that time is as maleable as space.

To see this graphically, observe the image above. Since scientists are only humans, they have difficulties imagining warped 4 dimensions, and so 2 dimensional analogs are used, which are enough to illustrate the point. The image above shows a distortion in space-time.  These imaginations of space-time were first thought of as what are famously now known in science as thought experiments, with one of the most popular users being Albert Einstein himself.

Then there’s Gravity

General relativity describes gravity as a curvature in space-time and that, again in a nutshell,  gravity is a dent in space. To further picture this, consider again the image above. Ordinary matter, which makes up everything we see in the universe, causes space-time to warp and bend around it. The more matter there is in a given object or point, the more warping, denting,  and bending of space time, and therefore the stronger the gravity. The image shows the Earth, which is relatively quite massive, making a dent in the space-time continuum, thus creating a gravitational effect which pulls us, the moon, and other objects in space towards it, even including the Sun. The Sun of course has the strongest gravity or pull in the Solar system, since it’s the most massive object in it. Again, remember that the image is just a 2D analog of a 4D space-time continuum. The Earth does not immediately plummet towards the Sun since the Earth has its own gravity, which counteracts the Sun’s pull. But nevertheless the Earth is slowly circling down the drain/dent of the Sun in the space-time continuum (Sun’s gravity) and in a few billion years, the Earth and everything less massive than the Sun will quite likely plummet towards it. In other words, gravity is just an illusion since we can’t quite really conceive a 4th dimension in our minds, and that gravity is really just a warping of the space-time continuum.

You can then further imagine or create a thought experiment that other less or more massive bodies than the Earth in the Solar system create their own dents or warps in space-time. These include the other planets, asteroids, and even us humans, albeit in a very minute fraction only.

In fact, one of the suggested ways of mitigating a future asteroid impact on Earth is based on the premise that mass causes denting or warping in space-time. The gravity or gravitational tractor, as it is known, deflects an asteroid many years prior to its impact on Earth, by simply hovering or “parking” beside the asteroid. This form of asteroid mitigation does not really require cutting edge scientific discoveries or engineering feats, it does not need to physically contact the asteroid, and does not necessitate the need for the mechanical and structural composition of the asteroid in advance. Simply put, it works by allowing the relatively massive object, the gravity tractor, to “pull” the asteroid towards a direction which will lead it away from a future Earth impact. The “pull” comes from the fact that, slowly but surely, the tractor’s warping of space imposes a pull, albeit tiny, to the nearby asteroid.

Finally, Falling in Love

So, by now perhaps you’ve already surmised my coy and sly use of the words “falling” and “attraction” with respect to falling in love, as well as how physics currently views gravity and space-time. In other words, geeks and nerds like me often joke about how a girl could “fall” for you if you simply sit near her, since you do have mass, however minute. That mass of yours will eventually make her notice you, or perhaps not, but it will certainly impose a “pull” on her towards you, or vice versa. Of course technically speaking, it will take millions to billions of years before the more massive one between you two finally pulls the other. In this case, it’s better if you just ask her out, and that sometimes physicists, geeks, and nerds like me don’t really give that much good an advice. Still, as I mentioned earlier in this article, phrases such as “I’m falling for you” and “We’re attracted to each other” are quite scientifically accurate. Ah, love in geek or nerd speak. So romantic.

Which brings to mind the fascination of some men in today’s times to skinny women. Based from what I’ve pointed out here, it’s physically (by this I mean in physics) understandable why some men would prefer heavier or more massive women, but what about skinny women? I suppose the social sciences have more to learn and discuss in these matters.

Resources, references, and further reading:

• The source of it all, The Project Gutenberg EBook of Relativity, Albert Einstein Reference Archive, ‘Relativity: The Special And General Theory’ by Albert Einstein (1916).
• Wikipedia article on space-time and General relativity.
• Wikipedia article on the gravity tractor, which is one of the many suggested ways to mitigate an asteroid impact on Earth.
• Best selling science book with easy to understand explanations of the cosmos, which includes descriptions of space-time,  ‘A Brief History of Time‘ (1988) by Stephen Hawking, Bantam Books. ISBN 0-553-38016-8.

This post will attempt to repeat, clarify, and elucidate the need for the remembrance and understanding of the phrase “correlation does not imply causation”. Scientific studies will be given, and the words in the phrase, which vary in meaning depending on usage, will be defined accordingly.

Scientific studies

Please take a moment to go through the following actual, summarized scientific research results:

1) In a previous scientific research using quantitative assessment, numerous epidemiological studies showed that women who were taking combined hormone replacement therapy (HRT) also had a lower-than-average incidence of coronary heart disease (CHD), leading doctors to propose that HRT was protective against CHD.

2) From a study at the University of Pennsylvania Medical Center, young children who sleep with the light on are much more likely to develop myopia in later life.

We will get back to them in a moment. Now we focus on correlation or co-relation, and why scientists, statisticians and skeptics, at the very least, should always maintain and promote the phrase “Correlation does not imply causation”.

Getting the words right

Now we’ll define the more important words in the phrase, so as to remove confusion. The definitions of the words will also help my point, which includes highlighting the confusion between correlation and causation.

First we review that correlation, according to merriam-webster.com is

“a relation existing between phenomena or things or between mathematical or statistical variables which tend to vary, be associated, or occur together in a way not expected on the basis of chance alone”

Which I will suppose is a fairly permissible definition of the word in casual discussions. Next, we will define what correlation means in mathematics, particularly in a statistical sense:

“it indicates the strength and direction of a linear relationship between two random variables.”

and that

“it refers to the departure of two random variables from independence”

Which I again will suppose is fairly permissible in a mathematical discussion.

The casual or colloquial definition of correlation generally means the existence of a relationship which may not necessarily be, as defined by mathematics, linear in nature.

Now that we have those out of the way, we move to the definition of the word “imply”. The site merriam-webster.com gives the following as some of the definitions of the word “imply”:

: to involve or indicate by inference, association, or necessary consequence rather than by direct statement

: to contain potentially

And the word is listed as synonymous to “suggest” and “infer”. This is how we would normally use the word “imply” in casual discussions, and I will suppose that it will be acceptable for such usage.

Now we define what “imply” means in a mathematical sense, or when used in logic:

To be a sufficient circumstance.

It is worth noting that, especially in mathematics and logic, correlation is a requirement for causation. But the reverse is not necessarily so, as we shall soon see. Correlation therefore is not the same as saying, in mathematics and logic, that if p then q, or rather that if p is true, then q must necessarily be true as well.

It is very  important therefore to note the difference between the casual use of the words from their scientific or mathematical use. In this article we refer to the mathematical or logical definitions of the words.

I repeat, correlation does not imply causation

The fallacy comes from the fact that people, including even seasoned scientists, often fall prey to the mistake of immediately  assigning causality between two correlated objects or events. Of course, when two objects or events are correlated, it cannot also be dismissed that there is no causal link between them. But the point still stands, that we tend to overlook other variables which, unseen or improperly observed, can be mistakenly dismissed, thus committing the fallacy.

I think one reason why a lot of us, again including even some scientists themselves, fall into this messy problem of causality and correlation is that, to a varying degree our brains are “biologically wired” to interpret patters. When we see a linear looking object between or beneath two rounded objects we more or less immediately see a face (happy, sad, whatever). When we look at clouds we are quite likely to see patterns. Same thing happens with correlation. We immediately infer and “jump to conclusions” that since object/event A is correlated with object/event B, they must be causally linked.

In fact the two types of correlation, positive  (when one variable increases/decreases, so does the other one) and negative (when one increases, the other decreases and vice versa) correlation I think does not make it easier to see through the fallacy of outrightly assigning causality when only correlation exists.

To further prove the point up to the point of absurdity, consider the correlation of your feet size and your intelligence. One could foolishly assume that, since feet size is correlated with intelligence, that the larger your feet size the smarter you are. Imagine what a surprise that would entail if it were really true. The fact is that as we do grow older and our feet size grow larger, we more or less become more intelligent, usually relative to what our intelligence was when we were babies for example. This is an example of a positive correlation with no reasonable causation.

An example of negative correlation with no reasonable causation is stating that the decrease in hair i.e. hair loss is met with an increase in senility. As your hair count goes down, your senility goes up. The fact that you get old and you lose hair does not necessarily cause senility, but that they just happen to happen together, correlated in a negative way.

Why not causation? (plus the scientific studies at the start of this article)

We now move to the  obvious reasons as to why correlation does not necessarily imply causation. One reason is that there may be a 3rd, 4th, and so on number of variables involved, and which were overlooked by the experiment or research. These variables then turn out to actually cause the causation betwen the correlated variables A and B. Another reason, which is actually an extension of the first one, is coincidence. By this we mean that the relationship of A and B are so complex and “un-unravelable” so as to consider them coincidental. Another reason is that A contributes to the occurrence of B, but is not the sole cause of B. In other words, if variables or occurrences such as these cannot be known or  studied more closely, the observation data alone cannot justify a causation between A and B.

Scientific example 1 (above) turns out to be a correlation but not a causal event. Re-examining the data, it was found out that the women who underwent HRT were more likely to come from higher socio-economic status, thus they tended to live a relatively healthier lifestyle via better diet and exercise opportunities.

Example 2 (above) regarding myopia on children, was later re-examined at the Ohio State University wherein they didn’t find a causal link between having the light on during bedtime and the occurrence of myopia later on. The newer study however found a strong link between myopia in the children’s parents and the development of myopia in their children. The study noted that the parents with myopia were more likely to leave a light on in their children’s bedroom, further elucidating the source of the correlation and confusion. Thus it was finally found out that the case of child myopia and the leaving of light/s on in the children’s bedroom are caused by parental myopia.

What’s the point of all this again?

But then you ask, if even seasoned scientists fall prey to this mistake i.e. immediately jumping from correlation to causation, how should a regular guy/gal like me fare otherwise? The point of this article is to promote healthy skepticism, which starts by not taking every word that comes from an authority figure, no matter how professional or experienced that figure is, as the gospel truth. I’m quite sure that, since you can read this article on the web, you can quite surely read other articles, my resources and references below, search the Internet and so on regarding a certain scientific topic or discovery or research result you just read.

I think this is a very important but easily overlooked phrase, since it could lead to confusion, fear, anxiety, hysteria and so on. The scientific examples given above probably only gave women and parents something to worry about. But consider for example a scientific study correlating the color red and child aggression. If improperly informed, parents, teachers etc. could storm their children or their children’s belongings, scaring or worrying children in the process, based only on correlation and not causation.

Resources, references, and further reading:

• Technical Brief on the 1999 Statistical Model, InfoWorks on “Correlation does not imply causation”: http://www.infoworks.ride.uri.edu/1999/techbrief/techbrief_8.htm
• Beyond The Rhetoric article on the phrase: http://btr.michaelkwan.com/2009/01/10/correlation-does-not-imply-causation/
• Types of correlations, from “SPSS Survival Manual: A step by step guide to data analysis using SPSS” by Julie Pallant, Google books.
• Nice Wikipedia article on the phrase: http://en.wikipedia.org/wiki/Correlation_does_not_imply_causation
• On the correlation of HRT and CHD, International Journal of Epidemiology,  33 (3): 464–7.10.1093/ije/dyh124. PMID 15166201
• CNN, May 13, 1999. Night-light may lead to nearsightedness: http://www.cnn.com/HEALTH/9905/12/children.lights/index.html
• Ohio State University Research News, March 9, 2000. Night lights don’t lead to nearsightedness, study suggests:  http://researchnews.osu.edu/archive/nitelite.htm

This short post is about the dilemma a coworker of mine just had this morning regarding network packets, and a not fully functional IPCop Linux installation.

The Dilemma

The server runs IPCop, which allows a PC to run as a firewall appliance. The IPCop server has 2 NICs, eth0 and eth1. Eth0 is connected to a Class A private LAN while eth1 uses a Class C address to connect to the public Internet. The problem however is that the Internet is accessible (Google, Yahoo! etc.) but not private LAN machines and addresses.  The private LAN’s gateway return ping replies, but not the DNS server.

Detective Work (i.e. Troubleshooting)

What I did was to check all possible causes for this problem: restart the network, checked logs for error messages and others, though some of these had already been done, but I just want to be doubly sure myself. I next checked the firewall using the iptables command. There were tens of lines of firewall rules, along with numerous chains. Since I was in a hurry at that time, I decided to skip the detailed checking of the firewall rules for the moment, even hough I have experience dealing directly with iptables, and not with the higher level application firewalls that just modify it. Next I tried to ping again the DNS server. Adding a -v in the ping command to make it more verbose, I noticed that packets were being successfully sent to the DNS server, but no packets were coming back. I thought to myself that the iptables firewall is one good suspect for this, but I’ll try a few more checks before I go to the nitty gritty of iptables firewall rules. I did ifconfig ethX up and then  down but to no avail. Replace the X with the NIC number you wish to up/down.

The Fix

I next checkd the routing table using the very useful route command. The static IP route looked fine, but I noticed that it was rathe incomplete, given that it has 2 NICs. What I mean by incomplete is that the route from the public, Class C network has routes for going in and out of the destination network and host, but the private LAN doesn’t have a route for traffic going into the IPCop server. It only has a route for traffic coming from the Class A private LAN NIC. Bingo was its name-o. Apparently the reason why ping packets weren’t making their way back to the IPCop server was that they weren’t being routed correctly back to the IPCop server itself. This was further supported by using the traceroute command. I traceroute-ed the private LAN DNS server and as expected, the routing of the packet was all messed up. The traceroute packets for the private LAN DNS server were exiting through eth1, and out to the public Internet already. No wonder it doesn’t have a private LAN connection!

So the fix was to add a correct route to the routing table using the route command. The new route should, well, route the packets correctly from the  private LAN back to the IPCop server, and to make sure that the class A private LAN traffic enters/exits via the eth0 NIC. To do this the command

route add -net NETWORK netmask NETMASK gw GATEWAY

was used. Just replace NETWORK, NETMASK, and GATEWAY with the appropriate values for your network. In our case, NETWORK was the destination host ( the local machine, given by 0.0.0.0) and GATEWAY was the gateway of the Class A network of the private LAN.

Sure enough, after adding that static route, the Class A private LAN became accessible.

This post is about a web article which mentions a technique that allows you to estimate, to a relatively good degree, your distance from another object. I’ll then explain the minor error which the article has, as well as the assumptions of the technique which the web article did not mention.

The Technique

I came across this neat trick from lifehacker.com about estimating distances using your arm and thumb. It is quite useful, but below I will outline a relatively minor error of the article, particularly the diagram used. It was a minor error but it still strikes me as something that should be brought to light, since it’s pretty trivial too. The original article btw was taken from the almanac.com article of the same name. Both articles were quite short so they only took me a small amount of time to read through them and to quickly notice that there was something wrong with the diagram.

The articles emphasize the fact that one’s arm (held straight) is approximately 10 times longer than the distance between your eyes. The articles also mention that with a bit of applied trigonometry, one can estimate distances between you and an object which you have a reliable width knowledge of. Unfortunately the article writer/s might have focused on the trigonometry part too much, overlooking their basic geometry when they created the diagram.

Here is the original almanac.com diagram showing a man estimating his distance from a barn which he originally knows the approximate width.

How The Technique Works

In case you haven’t read the original article yet, it basically says that (again from almanac.com):

• Hold one arm straight out in front of you, elbow straight, thumb pointing up.

• Close one eye, and align one edge of your thumb with one edge of the barn.

• Without moving your head or arm, switch eyes, now sighting with the eye that was closed and closing the other.

• Your thumb will appear to jump sideways as a result of the change in perspective.

How far did it move? (Be sure to sight the same edge of your thumb when you switch eyes.)

• Let’s say it jumped about five times the width of the barn, or about 500 feet.

• Now multiply that figure by the handy constant 10 (the ratio of the length of your arm to the distance between your eyes).

Now you get the distance between you and the barn—5,000 feet, or about one mile. The accompanying diagram should make the whole process clear (shown above).

The Error In The Original Diagram

The error comes from the fact that the original diagram, whether it be the vertical one from almanac.com or the horizontal, modified version from lifehacker.com, show the distance line not being parallel to one line common to both triangles formed. To see this more clearly, I’ve created a little more technical and descriptive diagram below. The new diagram shows, correctly, that the distance line (containing the 5000′ and 20” distance markings) is parallel to the line connecting the observer’s left eye to the barn’s new location. That’s it. That’s the error It may seem trivial, and it actually is, but I couldn’t help noticing it, especially since apparently no one has commented about it, and some people I know who should have noticed it, didn’t. The original diagram shows the left-eye-new-barn-location line to be non-parallel to the distance line, which is wrong, and which quickly caught my skeptical eye. Basic geometry will tell you that my new diagram below is the more correct one.

Assumptions Which Were Left Out

The assumptions which the article does not mention include:

1. One knows a relatively precise measurement of the object’s width, or that one should know a good deal about the object’s width before attempting to estimate distance with this technique. To see how this can become a problem if not entirely taken into consideration, suppose you estimated or falsely remembered that the barn was 400ft instead of 500ft. That would translate to your estimated distance of 4000ft, which is 1000ft shorter than the correct 5000ft! You’d then get a nasty surprise since you left out 1000ft. In other words, since the ratio of the object’s width to the distance between it and you is 10, your width estimation errors (again, could be from wrong estimation or remembrance of the object’s width) get translated to a distance error multiplied by 10.
2. The topography of the terrain. This technique assumes or works best in a plain, since if you were say in a hilly or mountainous region, the distance you’ll get from this technique is the straight line distance from you to the object. But it does not take into consideration the slope, nor the crests or troughs of the land. You may get a distance of 1000ft between you and the object, but if there are hills and such between you and the object, you know it will be more than 1000ft.

Gracias a mis amigos Rudolf y Aaron. Thanks to my friends Rudolf and Aaron for their quick help in confirming this error, since I wanted to be triply sure.

The original Star Trek TV series simply known as, Star Trek The Original Series (TOS) and  which started airing in 1967, is one of the great backbones of sci-fi media in my opinion, whether it be film or television. The series was riddled with attempts (sometimes successful sometimes not so in my opinion) of profundity, and at times humor.  The themes of several episodes are recurring themes in succeeding sci-fi series and movies. The series though was conceived as a ’serious’ primetime science fiction series, which I think means adopting or applying currently known scientific facts and researches at the time, instead of more often than not making things up without scientific temperament.

Here now is my list of the most physically attractive females (enemy or friend) in the whole 3 seasons of the series, in no particular order. Note that these are only the one-time female characters who are not part of the enterprise’ crew, as otherwise I would have included the lovely Nyota Uhura and other officers.

1. Nona from the second season episode of Star Trek The Original Series (TOS) entitled “A Private Little War“. She was played by actress Nancy Kovack. Interestingly enough, Nancy has quite a similar last name to a certain famous Watchmen character.   Unfortunately Nona became an antagonist and died for it. Still, she had a really beautiful face and a wonderful body

2. Eleen from the second season episode of Star Trek The Original Series (TOS) entitled “Friday’s Child“. Eleen was played by the beautiful Julie Newmar who is more famously known as one of 3 women who played Catwoman in the 1960s live action television series Batman. Eleen started as an antagonist though she decided to become otherwise at the end of the episode. Eleen was very beautiful, not to mention the way she pronounced Bones’ last name was really hot. She pronounced it “Mac-coy” in a very sexy way

3. Miramanee from the third season episode of Star Trek The Original Series (TOS) entitled  “The Paradise Syndrome“. Miramanee was a hot female Indian who seemingly became Pocahontas to Captain Kirk. In fact, she was so hot that Kirk had a child with her. Unfortunately, she died at the end of the episode

4.Zarabeth from the third season episode of Star Trek The Original Series (TOS) entitled  “All Our Yesterdays”. Zarabeth was a lonely woman who was sent back in time to live in a cave amidst an ice age, since her planet at the time she came from was about to end. Thus she lived alone wearing only loin clothes. She had a very pretty face with a nice body. Thank you loin clothe

Comments in a ruly manner are most welcome

I was actually backing up my WordPress (WP) posts, tags, comments, etc. via the Export option in the Administration page when I stumbled into this poem. The backup was just in case I set up my own WP installation, say in my own domain. Nevertheless, I also tried downloading some pages of my blog that had images, particularly logos, which weren’t really stored in my WP blog but were instead taken from other sources in the web, via the HTML tag <img> and its parameter src.

Then came a surprising revelation: if you try using the current version of WP, Kubrick, and then you check the style sheet: you’ll be confronted with this nice, witty and funny poem (at least in my opinion) about a guy probably wanting to marry a girl:

/* “Daisy, Daisy, give me your answer do. I’m half crazy all for the love of you.
It won’t be a stylish marriage, I can’t afford a carriage.
But you’ll look sweet upon the seat of a bicycle built for two.” */

It’s at the bottom of the file style.css, which you can get by saving any page from a WP site using the Kubrick theme (and perhaps other themes made by Michael Heilemann, the maker of the Kubrick theme). You can actually see it for yourself by saving the page you are viewing now. Check the source code of the page you just saved (i.e. my web blog page) and then view the contents of style.css. Voila! The short poem above appears at the bottom, perhaps written by Michael Heilemann himself.

Of course this poem might be very famous and well-known already even though I’ve only found out about it just now. You’ll have to excuse my not so wide ‘circle’ of information sources.

I should try adding poetry sometime in the source codes of my software projects. Maybe I’ll do so now…

This will be a quick post/note-to-self since I’m pretty occupied. Actually, the title of this post should have been “How to bloody fix the deceptively easy but hard to find confounding error in PHP headers: “warning Cannot modify header information – headers already sent”. But that’s too bloody long (though it would be interesting to find out in the future how WordPress concatenates long URLs…). The reason why I call it deceptive will be clarified at the 3rd entry below

The 2 primary parts of an HTTP request response are the headers and the body, which should be sent separately. Now in PHP sometimes some programmers, not just novice ones but long time ones (ehem…like me…) forget that we’re modifying them programmatically, which can sometimes cause errors. The header must always be sent first before the body, wherein both are coming from the web server. This is highlighted in this Wikipedia HTTP request example. For example, the php function header() can modify some of the (obviously) header parameters, most/all of which are listed in this Wikipedia list of HTTP headers. The above PHP error occurs because the body (or part of it) has already been sent by the server to the client, afterwhich a change of header values follows, either from the client or server.

Now, to finally fix the deceptively easy to fix but hard to find source of the error

Warning: Cannot modify header information – headers already sent by (<some of your PHP source files should be listed here>)

You can check the following:

1) If you’re using the header() function or some PHP function that modifies the header or controls the flow of action of your pages (e.g. from one page to another), you should inspect those. Usually it’s better to use conditional statements (e.g. IF or ELSE) to isolate the execution of one part of your code from another. It is quite likely that the error comes before or at the line of this function.

2) Make sure you don’t output/print/echo anything to the client (body) before sending/changing the headers. Again, conditional statements are useful here.

3) Finally, and the easiest to overlook, is to remove any white space outside the PHP start and end tags (<?php ?>). This is quite often the easiest thing to miss (for me at the least). The reason for this deceptive white space causing an error in PHP is that the white space is still interpreted as an echo statement printing a blank line, which interrupts the format of the HTTP header (see Wikipedia header format example above).

Of course the disclaimer here is that you are to most likely encounter this error if you’re more or less building your PHP application from the ground up, or without using web frameworks. It’s more unlikely and unusual to receive this error while you’re using an MVC based PHP framework.

As you all know, a lot of people, creative in art or not so much, create and use ASCII art ranging from the complex (machines, sceneries, human faces) to the trivial ones (faces, smileys: (^)__(^) d(o)_(o)b ). Now I’ve been looking around the Internet for a Vulcan salute ASCII art that really appeals to me. I mention appeal because the Vulcan salute ASCII arts I’ve seen so far are not so convincing, i.e. they don’t really look very much like the real salute (of course this is obviously a subjective thing).

Some of the Vulcan salute ASCII arts I’ve found are the following:

This one involves an underscore followed by 2 forward and backward slashes (source: http://www.geocities.com/dronak/smileys.html)

_\\//

This next one has one version similar to the above art, while the other version uses a “les than” symbol ‘<’ to introduce the thumb (source: http://en.allexperts.com/e/e/em/emoticon.htm)

<\V/ or \V/_

As I’ve mentioned, I’m quite displeased with the above Vulcan salute ASCII art and so I created my own versions. The following are my two versions with specifications describing them and how they are made:

My version 1

_\\//()

\V/,

Specifications: This version uses backward and forward slashes to represent the pinky and the index finger, respectively, while the capital letter ‘V’ represents the ring and middle finger. Lastly, a comma represents the thumb. I used the comma for the thumb, and not an underscore like the above versions, since the thumb is usually not angled that much from the index finger in a usual Vulcan salute. In my version the forward slash (index finger) has a much smaller angle/opening with respect to the comma (thumb) compared to using a forward slash with an underscore. The smaller angle/opening is in my opinion, the correct form of the Vulcan salute as shown by Spock in this image.

My version 2

\\//,

Specifications: This is quite similar to the first  version I mentioned at the start of this post. That is, slashes represent the four fingers with the exception of the thumb. The differentiator is also the comma representing the thumb, which again has a look closer to the way a Vulcan salute is done.

License

Finally, I license my 2 ASCII art versions of the Vulcan salute under the following Creative Commons licenses listed here:

• Attribution (by): Licensees may copy, distribute, display and perform the work and make derivative works based on it only if they give the author or licensor the credits in the manner specified by these.
• Noncommercial or NonCommercial (nc): Licensees may copy, distribute, display, and perform the work and make derivative works based on it only for noncommercial purposes.
• ShareAlike (sa): Licensees may distribute derivative works only under a license identical to the license that governs the original work. (See also copyleft.)

That is, under the Attribution + Noncommercial + ShareAlike (by-nc-sa) licenses of Creative Commons.

Comments and suggestions are welcome as long as they are calm and ruly.

And, as is the customary farewell among Vulcans,

Live long and prosper \V/,