Genius

WARNING SUBJECTIVE POST!!

This man is an absolute genius.

The album (Tubular Bells II) was recorded with just him playing ALL instruments, rerecording it time and again, in his own studio.

Take a look at how many musicians (keyboards, etc) are needed to perform the same thing LIVE.

John Gordon Sinclair joins Viv Stanshall (RIP) and Alan Rickman (Hans from Die Hard)in the announcement of the instruments. The post person spelled "Edinburgh" wrong

Note the change in guitar at the end. Wonderful! Note also the way he plays the guitar. Side swiping the strings, not up and down (Space Invaders???) and unique.

That GUT feeling

For centuries, well, decades, at least, mankind had striven to find a theory of "everything". That is, one single math formula that describes all of physics.

That goal is still some way off, despite massive strides that have been made towards it.

The argument goes something like this:

A total of four different forces have been identified. Please note as opposed to the previous post, these are specific kinds of force, whereas the previous post dealt with the CONCEPT of a force.

These four "types" of force hold the Universe together. However, they are somewhat limited in various ways.

In detail, these are they:


The Oldest known, Gravity. It acts on everything and is always attractive.

The next to be studied was Electricity, or as it is now known, Electromagnetism. This acts only on stuff that is electrically charged. That is, stuff that is not neutral electrostatically. We do not know what charge "is" yet, even today, just that stuff with the same "charge" repel, and stuff with opposite "charge", attract. There are only two of them

The third force is called the "strong" force, is always attractive and acts only on stuff that is desperately close.

The fourth is the "weak" force (we ran out of names long ago) and only acts on radioactive stuff (it causes atomic nuclei to split up)

There are no others

Each of these "forces" has it's own set of equations that describe only it (electromagnetism has four of its own)

It has long been a dream of all science to unite all these equations into one.

It has not been done yet.

They all seem to have two things in common, though. They all have a specific "range" and all use "exchange particles" to be felt. That is except gravity. Gravity has infinite range, but no "exchange particle" has ever been detected.

There may be hope, though. In 1974, Steven Weinberg and Abdus Salaam (I forget the name of the third), managed to marry the "weak" force with electromagnetism, calling it the "electroweak" force. The prediction, if this were true, would be three new "exchange" particles called the W+, W- and the Z-0. It wasn't until 1983 that we had the particle accelerator powerful enough to produce them, as they were predicted to be very heavy (E = mc squared, after all). Sure enough, they turned up.

So we had three forces now, not four.

There have been reliable equations suggesting that the "electroweak" can be married to the "strong" force, although to prove this we would need an accelerator the size of the galaxy to detect these exchange particles (dubbed the "X" particles)

However, there was another prediction from this marriage - proton decay. Protons are to all intents and purposes, stable, although the other one, the neutron, decays in about 16 minutes.

If the Electroweak and the Strong forces, were really part of a bigger picture, the proton would have a half-life of about 100000000000000000000000000000000 years (1 followed by 32 zeroes).

Since the universe is only about 15000000000 years old, none would have gotten round to decaying yet, UNLESS we watched 100000000000000000000000000000000 protons for a year.
Us peeps have been doing this for maybe a decade now, and so far no results (it is very hard to detect just one amongst all those, even without red herrings coming from just about everything else.)

If we do detect proton decay, we will only have gravity to deal with.

That is the be-all and end-all. Gravity, almost like an unusually stubborn mule, blatantly refuses to conform.

Ok, so there may be a way out by conjecturing "m-theory", "brane-theory", and "string-theory", but to prove this requires travel in eleven dimensions. In other words, these are only words, not proof.

Warning! SUBJECTIVE STUFF!

Gravity differs because it is geometric as refined by Einstein. The other three are gauge FIELDS, and require exchange particles to be felt.

Geometry by definition does not require exchange particles and I am surprised that even Einstein tried to meld his own theory with the other established forces. Maybe it was peer pressure.

END OF SUBJECTIVE STUFF

Suffice it to say, we do not really have a Grand Unified Theory (GUT) yet, although we may have one for everything except Gravity.

The whole picture can be summed up in an energy diagram (see below), as we believe all the forces were one once, when there was so much energy there was no distinction. As the Universe expanded from the Big Bang, the amount of energy decreased (per cubic meter) and the forces separated in a process known as "symmetry breaking". Th.e diagram shows that gravity is conjectured to be there, but that is more like hope than speculation

We try to address this by putting lots of energy into our particle accelerators to maybe recreate conditions as they were during the big bang.



We still have a GUT feeling one is out there somewhere. Lord knows, we've tried!

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.