Thunderstruck

Many times in the movies the word "Force" is used (most often in "Star Wars")

But just what is a "force", in physics terms?

It takes a bit of understanding to realise what is happening.

Newton's second Law says that "force = mass x acceleration"....

...but what is "force" ?

A simple example may give an introduction.

It can easily be put into words:

A "force" is " a push which does not stop pushing".

A simple example of which is a car engine.

It "pushes" the wheels against the ground and goes into forward motion. The pushing power is maintained in the gas pedal. Remove your foot, the pushing stops, and the car rolls to a halt because of another "force" - friction. Friction pushes the car the the other way. (if it did not, we would have created "perpetual motion")

So, to keep the car going, it has to push along ALL THE TIME just to keep at the same speed.

In short, a "force" is just "a push which does not stop pushing".

In space, it is different because there are almost no "opposing" pushes, such as friction.

This is why, in space, one "push" is enough.

Point the craft in the direction you want it to go, and use one push (this is called "impulse"). It will go without stopping (Newton's First Law) at a speed that does not change.

If you want it to go faster, keep pushing, and it will. This kind of push is "force", and the longer you maintain this push, the faster the craft will be going when you stop the push.

But supposing you do not stop pushing?

This is the definition of "force". It does NOT stop pushing.

Do we get this in nature? We sure do. Electrostatics is one of the examples. Lightning happens because the electrons cannot stop being pushed to the earth by the "force" of the attraction to it. So the electrons invent their own way of getting there, and the effect is a bolt of lightning (sorry, Doc Brown). The reason that the lightning is never straight is simply because there will always be obstacles, such as as pressure differences, clouds, temperature etc.

This is the best way to view a force. Watch a thunderstorm.

Be thunderstruck!

The Location of Meaning - The Stony Rosetta.

(Apologies to Douglas R Hofstadter)

Below is a selection of meaningful sentences in some of the more obscure languages.


Uppermost on the left is an inscription in the undeciphered boustrophedonic writing system from Easter Island, in which every second line is upside down. The characters are chiseled on a wooden tablet, 4 inches by 35 inches. Moving clockwise, we encounter vertically written Mongolian: above, present-day Mongolian, below, a document dating from 1314. Then we come to a poem in Bengali by Rabindran Tagore in the bottom right hand corner. Next to it is a newspaper headline in Malayalam (II Kerala, southern India), above which is the elegant curvilinear language Tamil (F Kerala). The smallest entry is part of a folk tale in Buginese (Celebes Island, Indonesia). In center of the collage is a paragraph in the Thai language, and above it a manuscript in Rn dating from the fourteenth century, containing a sample of the provincial law of Scania (so Sweden). Finally, wedged in on the left is a section of the laws of Hammurabi, written Assyrian cuneiform.

The diversity of language is almost as widespread as the cultures that produce them.

Glory Be!

This image appeared today on Yahoo as a "rare" image.

However, it is only "rare" as in having rarely been photographed.

The fact is, every rainbow is different.

Different in the sense that the person standing next to you sees a different rainbow which has different "ends".

I was travelling in a minibus on a freeway once in the rain whilst the sun was shining. I looked behind the vehicle as I knew there would be a rainbow there.

And there it was, but it was travelling with the vehicle!

It's end was in the verge and it's diameter was about 4 or 5 meters.

I alerted my friend, who was sitting on the other side of the vehicle. He noticed it too, but HIS rainbow ended on the freeway.

The rainbow is only part of the thing called a "Glory", which in normal terms would be a completely circular rainbow.

Normal rainbows are only partly seen "Glory's". You have to be in the air to see a Glory.

Here is an example:



Now THAT'S a rainbow!

The Mandelbrot Set

No, this is not a picture of a beetle, but a picture of the mathematical concept of the MandelBrot Set, named after Benoit Mandelbrot.

It has the property that no matter how much you zoom into it, it looks either the same or similar, all the way up to infinite magnification.

Click HERE to try it!

The origin of this "set" of "points" is beyond the scope of this blog, but suffice it to say, it is plotted from a recurrence relation on the complex plane.

In ordinary language, a "recurrence relation" means that a math formula is fed it's own answers over and over again, and each result is plotted on paper. It's a bit like a snake swallowing it's own tail.

"Complex" refers to the type of plotting needed, as it only works with special numbers called "Complex Numbers".

"Plane" simply means a flat piece of paper!

The different colors represent how near the numbers come to the black area, like contours on a map.

Fool around with the link, it's fun!

Draw this?

White (Akiko) to move.

I play Chess really rather well - NOT!

I have three chess computers but none will offer a draw.

I ask this of those chess-playing people who read this.

In snooker, it would be a re-rack.

Comments and analysis welcome.

Light does a Bender

Gravity bends spacetime (spacetime is 3 dimensions of space, one of time). In the diagram, the space is seen as two dimensions, and the earth bends it as if it were a rubber sheet.

If you have a black hole instead of the earth, the singularity inside the black hole actually punctures the sheet. A "singularity" is our name for classifying the unclassifiable. When matter is squeezed into nothingness, physics breaks down completely. The "black hole" is actually a name for the area inside of which nothing can escape. The terms "black hole" and "event horizon" mean the same thing, whereas "singularity" is the term for the thing in the middle of it all.

The straight lines in the diagram are called geodesics (light paths), and as is clear, they are bent.

So light, although composed of massless photons, is affected by gravity, because gravity is not really an attraction, but a geometric effect.

OPINION:

This is one reason why I believe gravity will never be united with the other three forces, which are gauge fields. Gravity is not a gauge field, but geometry.

A Degree of Latitude

It is a well known fact that in the UK, Japan, Korea and Switzerland, if you face the sun at midday, you are facing South.

On a visit to the Philippines once, I had an unusual experience.

My assistant, Raquel lives in Barangay Hilusig, in the center of the Island of Leyte, Visayas.

The bus from Tacloban City (1oo km away) runs right by her home on the concreted National Highway from Manila to Davao City. Believe me, it is a noisy highway, despite being halfway up the mountain and in the jungle!

In the Philippines, there are no bus stops, you just wait and flag the bus down.

I must have waited outside her house a dozen times before I figured out what was wrong.

In the Philippines, whose latitude varies between 6 degrees and 15 degrees (Latitude being the angle that the imaginary line between the center of the earth, the equator, and the place you are on the surface, makes. For example, the latitude of the north pole is 90 degrees, a right angle). England is about 55 degrees latitude, that is, much more to the north.

In the daytime, the sun in the Philippines is almost always directly overhead, being so far south.

The highway runs exactly North to South past Raquel's home, and I was standing on it, looking down it, in the southerly direction.

Then I noticed something really strange. It was midday, and being north of the equator, my shadow should have been behind me. But it was in front of me.

It took me the whole bus journey (90 minutes) to work it out:
























The Tropic of Cancer is there to indicate the extent that the Earth's tilt in space affects the climate. It is at 23.5 degrees latitude. At June 21, the sun is directly overhead at the Tropic of Cancer.

Since the Philippines is above the equator but below the Tropic, at some points in the year, the sun is actually NORTH when you face it, as the diagram shows.

This is what caused my shadow to be in front of me when I faced south.

The effect is subtle and directly related to the "midnight sun" as seen above the Arctic Circle.

Sines of the Times

Trigonometry is a mystery to a lot of people. First off, what is it in the first place, and second, what is it for?

First answer first: It’s triangles. It’s about how the sides join together and the way this affects the rest of the triangle.

Imagine a ladder leaning against a wall. How do you find the best way to lean it? If the first rung is too far away from the wall, the ladder will slip when you climb up. If the first rung is too near the wall, it will not slip, but the ladder will be harder to climb up. The best way seems to be a compromise. The “leaning factor” needs to be optimised. This “leaning factor” is a measure of how steep (or not) the ladder needs to be to be safe to climb up. This measure has a unit, and that unit is “degrees”.

For the ladder to be stable, it needs to be at about 60 degrees with respect to the ground (about 2/3 of a “square” lean (that is, if the ladder is vertical))

The picture that the ladder makes is called the “angle” it makes with the ground.

Trigonometry is just the study of relationships between “angles”. Questions have arisen, such as this: If my ladder is five meters long, how far up the wall will I be able to climb using the “optimised leaning factor”? Will I be able to clean that window which I know is exactly four meters above the ground?

The answer is “Yes” because the answer is that the top of the ladder will be at 4.33m up the wall.

Here’s the picture of what is happening:






The ratio of the length of the ladder to the distance up the wall is that same for all angles of “2/3 of a “square” lean”. In fact, these ratios are all the same for each “lean” you care to name.

They have names, too.

Here is a typical triangle they relate to:





The three sides are named (O)pposite, (A)djacent and (H)ypotenuse, and the ratios go like this:

Sine = Opposite/Hypotenuse

Cosine = Adjacent/Hypotenuse

Tangent = Opposite/Adjacent,

Or, as one of my students taught me, SOHCAHTOA.

But why bother? The answer is that the numbers have already been worked out, so if you do not know the angle but know the sides, you can look it up on the calculator. Also, if you know the angle and the length of one side of the triangle, you can find the length of the other sides as well.

Oh, one final thing, it works best if the triangle has one angle which is the same as the ladder standing up vertically.

That kind of “angle” is called a “right angle”, to give the right angle on things. Of course, the boffins figured out how to do all this even when the angle is not “right”, but that is not the point, not to put a too acute point on it.

Suffice it to say, sines, etc, go far beyond mere triangles, and in fact have more applications in math than you can shake a proverbial SOHCAHTOA at, but that would be a sign of going off on a tangent.

I can get along very well without such a program

Computers are so commonplace nowadays, many people do not understand why they are so useful.

Here is the rub, computers understand nothing but two numbers, a “1” and a “0”. They are just, when all said and done, a bunch of switches that are either “on” (a “1”) or “off” (a “0”).l

Humans do not see this level, All we see are games, photos, movies, etc.

But the real reason computers work is that these very zeroes and ones can be looked upon in more than one way.

It is similar to the USE-MENTION distinction in English. To elaborate, the word “bubblegum” is a word. I don’t chew it. I just look at the word. However, I DO chew bubblegum. The quotation marks signify the “mention” of the word, as without them, the word is actually “used” in the sentence – I chew bubblegum. It describes an action.

“bubblegum” describes the word. Bubblegum describes the product.

Computers understand the 1s and 0s in at least four different ways, in the same way that bubblegum above is understood in two ways.

Here is a short computer program in the computer language AKIKOKAKOLA to do the sum 1 + 1 = 2:

0001 PROGRAM STUPID
0002 INTEGER x, y, z
0003 x = 0
0004 y = 0
0005 z = 0
0006 PRINT “Hi, this program adds 1 and 1”
0007 INPUT “Please type in 1”, x
0008 INPUT “Please type in 1 again”, y
0009 IF ((x = 1).AND.( y = 1 ))THEN CONTINUE ELSE GOTO 0002
0010 PRINT “Thank you for your input”
0011 z = x + y
0012 PRINT “The answer is “, z
0013 PRINT “Congratulations!”

Line 1 is the program name (STUPID because it just does 1 + 1 )

Line 2 introduces x, y and z.

Lines 3 – 5 starts them off at zero.

PRINT outputs text to the screen. INPUT does the same but accepts numbers as well. Lines 7 and 8 ask you to type in “1”

Line 9 is the most important, It is a test to make sure you have typed in the two “1”s. If you did, the program CONTINUEs. If you didn’t, it makes a jump back to line 2, and starts again.

The last two lines give the result, 2.

All the words above are represented inside the computer as 1’s and 0’s. Here is where the USE-MENTION distinction comes in, only with computers, there are more than two meanings to the 1’s and 0’s.

The “x”, etc are regarded as data, i.e. information (numbers). INPUT, PRINT, GOTO, etc are “commands”, i.e. instructions. The 0001, 0002, etc are locations in logical steps to be done one after the other.

The most important aspect of computers is in line 0009. The 1’s and 0’s that are in the computer are here to be regarded as “locations” to be “jumped” to, depending on if the “data” inside the “x” and “y” is correct or not. It is this capability to “jump” unique to computers, as opposed to calculators, that enables more complex calculations to be performed (such as 2 + 2 = 4)

The point is that a sequence of 1’s and 0’s can be regarded as representing a number (1), a character (i.e. letter), an instruction (GOTO) or a location (0002 or 0010).

That’s four, so to revert back to our English language analogy, it could be termed the NUMBER-CHARACTER-INSTRUCTION-LOCATION distinction.

This is the sole reason why computers are so powerful.

Incidentally, there is no such computer language as AKIKOKAKOLA, I made it up, but the program principles raised here can be implemented in FORTRAN, PASCAL, BASIC, LISP, and even COBOL (in COBOL, there would be at least 70 lines, as opposed to my thirteen)

The age of writing bespoke computer programs is largely dead now, for the simple reason ICL implemented a package in the late 1980’s called “Quickbuild”, which wrote it’s own programs.

Writing programs is now limited to scientists who need to design simulations based on the latest models of how something works, be it galaxy evolution, black hole physics, or even something as humble as quantum mechanics.

It’s the Attraction

Many people do not understand electric charge. Maybe because it is enshrouded inside Physics. However, it is quite easy to explain.

There are two bits, and they are opposite to each other. If two of these which are the same are near each other, they push the other one away. If they are different, they clutch each other vehemently.

That is the basis of “Electrostatics”.

Having noticed that this happens, it was a logical step to find out how much they pushed each other away, or clutched each other (vehemently).

So the “push” or “pull” was measured with “pushing and pulling” measuring devices (“springs”).

For want of better names, we called each bit “positive” and “negative”. I think that “ding” and “dong”, or “Laurel” and “Hardy”, are much more interesting. I will stick with the latter because it is more fun.

So, Laurel-Laurel and Hardy-Hardy push each other away, and Laurel-Hardy love each other dearly.

But how much?

A Law emerged. It is named after two different scientists, depending on the certification.

Coulomb’s Law for the kids ( PG rating), and Gauss’ Law for the adults (18 rating).

The PG goes like this –

The amount of push (or pull) is found by multiplying together the number of all the Laurels and all the Hardys, and dividing the answer by how much distance there is between them. There ARE mitigating circumstances (such as you have to multiply this distance by itself before dividing, and then multiplying this very answer by something else which never changes), but in essence, this is Coulomb’s Law.

In Symbols, it becomes:


Where q1 and q2 are how many Laurels and Hardys there are respectively, and r is the distance between them.

Because Laurel and Hardy are opposite, we need to put a “minus” (“-“) sign in front of one of the numbers (it does not matter which). Then, because of the physics and math at work, the “push” answer is a number greater than zero, and the “pull” answer is a number less than zero.

That’s it! From these simple observations, all electricity began. Without this knowledge, there would be no lighting, music, television, computers, satnav, or even cars ( I will leave you to work the last one out).