random8042

Aspiring Polymath, Star-Craving Mad.

Quantum Physics re-explained

“Gremlins

“A new interpretation, presented for the first time here, is that there are little green gremlins hovering around, going backwards and forwards in time, shaking hands and collapsing with mirth as they poke and prod subatomic particles in a way they calculate most likely to confuse us. This explains all of the observed experimental results, but it does introduce gremlins, and the need for a further theory about why they should want to confuse us. Using the principle of Ockham’s razor, this interpretation will probably not find much popularity among the scientific community although it may be the basis for a new religion. Watch this space.”

http://www.higgo.com/quantum/laymans.htm

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The Anthropic Principle

Greetings, friends.

I now have 42 followers, and to celebrate I got a new wallpaper.  It is a picture of a sperm whale and a bowl of petunias against a background of sweeping and towering clouds.  Very dramatic.

To start, from Wikipedia: the anthropic principle is the philosophical consideration that observations of the physical Universe must be compatible with the conscious life that observes it.

The fact is, we exist.

And this a truly remarkable fact.  If the physical constants had been chosen at random, it is unlikely that life would exist, and less likely that consciousness would exist.

The fact that we exist means that the laws of the universe must be such that we can exist to observe these laws of the universe.  That is the goal of physics: to discover the laws governing the universe by experiment and observation.

Well, the idea of experiment and observation is relatively new.  The scientific revolution and all that.  Leonardo Da Vinci was a big fan of careful observation, but he was a little ahead of his time, in many respects.  Moving on.

One possible reason why we are here is that in an infinite multiverse, there must be some universes being observed by intelligent beings.  Those universes that are not observed are… well, not observed, so of course the one that we are observing is observed by intelligent beings, viz. us.  Do you see?

Another argument says that the universe “wants” to be observed, and it deliberately made its laws such that we could do just that. By the principle of Occam’s Razor (which I mentioned here) this is the weaker argument, as it requires the universe to have a consciousness of its own, to have desires, and to be capable of changing itself in accord with its desires. We humans struggle sometimes with the last of these.

Of course, nobody has yet discovered a reasoning behind the physical constants, they just are.  If there were a reason behind them, or behind the relationships among them, this might narrow the field of possibility to include a greater proportion of universes in which observers exist.  Or it might not.

So there you have it.

Bright Blessings.

Goodbye.

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Magnetic Monopoles

Greetings, fellow Earthlings.
You may (or may not) remember that last time I said I might (or might not) find the time to tell you about these wonderful pieces of curious science.
As it happens, I do appear to have that time.

Now, as you know, electricity and magnetism are more or less the same thing.  Ish.
They both exist in the electromagnetic field, and they both have two equal and opposite “charges.”  At least, electric charge is called charge.  In magnetism, you have North and South poles.

A magnet, you see, has both a North and a South Pole, creating the familiar field line shapes of woosh-woop.  I was waving my hands around when I typed that.  It would have made more sense if you could have seen me doing it.   This makes it essentially “neutral,” as the North-y charges cancel out the South-y ones.
In atoms, the positive charges of the protons are balanced by the negative charges of the electrons.  Technically, the positive charges of the up-quarks are cancelled out by the negative charges of the down-quarks and the electrons together.  Anyway, it is electrically neutral.
On a slightly bigger scale, you have things called zwitterions (SUCH a cool word!) which are neutral overall, but have separately positive and negative parts.  Amino acids in solution make zwitterions.
The point is, particles with a single, unbalanced electric charge are fairly commonplace.  So why not have a particle with single unbalanced magnetic charge?

Why not indeed?
So they did.  Using Bose-Einstein Condensates. (BECs.  It always makes me happy to mention then.  We have a running joke of:  Person A:”Hurry up!”  Person B:”I am hurrying!  I’m travelling at the speed of light…” People A and B:”…In a Bose-Einstein Condensate of the element Rubidium.”  As you can see, I have interesting friends.  By the way, light hardly moves at all in a Bose-Einstein Condensate of the element Rubidium.)

The magnetic field of a monopole looks like a star. *   Depending on whether it is North-y or South-y, the field lines either go out of it or into it, but either way they are just straight lines.  Nice and pretty.  Like evenly spaced radii of an infinite circle.
Magnetic monopoles behave in a magnetic field as electrically charged particles behave in an electric field (unsurprisingly.)
There is a prediction that if sufficient numbers were made to flow along together, we could make “magnetricity,” which They are calling “electricity’s little sister.”  Aww, cute… sibling rivalry.
And why not?

I am afraid that that is the limit of my knowledge on the subject of magnetic monopoles.

So, now for the irrelevant news-of-my-life part.
I am in the top five of a creative writing competition at school, but I don’t know exactly what place I got, or how many people entered (which was quite possibly five).
The theme was Fire and Ice.
My advice on creative writing:  surrealism.
That is all you need.  They love it.  My one is basically:  “I fall asleep.  I dream about Ice.  The Ice goes away and instead I dream about Fire.  The end.”  But with lovely lovely phrases in it like, “instrument of immobility” and “radiant anarchy.”  I had fun writing that.

What else is happening?
I read a book about Nothing.  It was a collection of random articles, covering cosmology, the placebo effect and the benefits of exercise.  Rather pleasant to dip in and out of for twenty minutes or so at a time.
It occurred to me today, when somebody told me that reading around the subject would be good for my CV that reading mathematical/scientific books and magazine article isn’t something I do for the sake of academic achievement any more, it’s just something I do, like reading science-fiction and fantasy and collecting pictures of dragons and listening to music.  (Bach’s Concerto In D Major For 2 Violins right now, but I enjoy a wide variety of genres).

Anyway, that’s enough rambling.
I will return later, hopefully with something to talk about.

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Supersymmetry

Hello!  Hello hello hello!

It’s so nice to see you again!

I’m feeling a bit flippant today.  One of my teachers told me that a piece of work I handed in was “a flight of fancy.”  That made me very happy.  And guess what happened?  Weirdest of weird:  somebody came up behind me in the corridor and stuck a carrot in my hair with sellotape.  I mean, what?  I didn’t even know her name.  Well, it just goes to show.  Quite what it goes to show, I am not entirely sure.  But still.

Well, now.  Supersymmetry.  Not to be confused, of course, with super symmetry.  Or wardrobes, for that matter.  Can you imagine the embarrassment of confusing your wardrobe with a sneutrino?  Or a squark?  But I am getting ahead of myself.

Let us suppose that you know what symmetry is.  Let us further suppose that you are familiar with the table of fundamental particles.  On second thoughts, don’t follow that link.  Is it astoundingly uninformative.  Okay.  So.  There are twelve fermions, arranged into three columns (the generations of matter) and four rows.  The top two rows contain the quarks, and the third and fourth the leptons (neutrinos in the third row).   The bosons are stuck on at the side, because they used to fit nicely before the Higgs Bosons was officially added.  Never mind.

Under supersymmetry, each of these particles has a superpartner, named after its cousin (e.g. the quarks are sup, sdown, sstrange, scharm, stop and sbottom).  I don’t know if the superantiquarks (antisuperquarks?  antisquarks? santiquarks? hippopotami?) are antisup etc. or santiup etc.   Probably the former.

Antimatter particles have opposite charge, but identical mass and spin to the antipairs.  Superpartners, on the other hand, have identical charge and mass but opposite spin.  I hope you understand at least half of this.  If not, please feel free to ask.  It is unlikely that you will receive an answer any time soon, but you are certain to lose nothing.

Another important difference between antimatter and supersymmetry is that supersymmetry is a mere hypothesis, whereas antimatter is a… theory, probably. I do not wish to repeat myself by getting entangled in the nature of scientific truth versus absolute truth.  (The empirical sciences, that is, not mathematics).

In other news, synthetic magnetic monopoles!

Wow.  Now they are interesting.  Maybe I will find the inclination to ramble about them on here some time.

Either way,

Dif-tor heh smusma.

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Gödel’s Incompleteness Theorem and its Implications in Linguistics

Don’t you just love a fancy title?

Well, I do.  That’s why I wrote it.

I came up with this idea a couple of years ago, dismissed it as paranoia, and forgot about it.  But it kept popping up in my head again.

Let me explain.

Gödel’s incompleteness theorem states that:

“No consistent system of axioms whose theorems can be listed by an effective procedure is capable of proving all truths about the relations of the natural numbers. For any such system, there will always be statements about the natural numbers that are true, but that are unprovable within the system.”

Comprendez-vous?  Chouette!

Yeah.  An axiom is a statement that you assume from the beginning to be true.  They are supposed to be self-evident, and then you use various logical methods to extract other statements from your list of axioms.  The trouble is, it’s very hard to get further than “I think therefore I am.”  You see, in order to say that you ought to also have a rule that says “everything which thinks is.”  It might seem obvious, but you then start to get into defining thought and existence, and it all ends up in a horrible mess.

That is the trouble with rationality: it can make you go mad.

Yes, anyway.  Gödel says that if you have a list of axioms, you can’t prove every truth using only that system that axioms.  For instance, you can’t prove your axioms, which you ought to do, really. At least, I think so.

If you start with only one axiom, and then derive something else from it, and then derive something else from that ad nauseum, and then you have something with which you can prove your first axiom, you might think you have proved all of your axioms, but now your proof of one of the axioms relies on that axiom itself.  And:

Circular reasoning works because circular reasoning works because circular reasoning works because...But it’s cheating.

 

Now for the paranoia.  Consider the dictionary.  What does it do?  It gives definitions of words.  How does it do that?  Using words, of course.  So how is possible to know for sure that you have fitted all the words together into their pattern in the same way as everybody else?  How do you know that the word “the” means the same to you as it does to anybody else?  Let alone complicated words like “counter-current multiplier mechanism” (which is something that happens in kidneys, by the way).

With no external reference point, like mime or pointing at solid objects, would it be possible to get words swapped around in such a way that a dictionary was completely self-consistent?  I don’t know, I haven’t even read all the way through my dictionary yet, so I haven’t even started trying to switch things about.  That would be tedious, complicated, and almost certainly futile.  Still, I find it a scary thought.

Luckily, external reference points do exist.  We learn our first words by associating them with changing environmental factors. Foods are usually mentioned just before they appear.  People’s names are usually used when the person talking is looking at a specific somebody else.  So the chances of getting everything skewed is even lower than exceptionally low.

The colours thing could be true, though.   People could have shifted perception so that their brain sees green at the wavelengths that other people see as blue.  And because we can only communicate about colours by their names or wavelengths or something else completely arbitrary (basically not a mind-meld) there would be no way to tell.  I don’t find that quite so scary though.

Imagine if everybody else were talking a different language that just happened to have the same words but with different meanings.  How scary would that be?  And what would have to happen for you to notice?  It’s crazy.  Maybe I’m crazy.  Probably. I have things that need doing.  Like proving that the sum of the reciprocals of any three positive real numbers is greater than or equal to twice the sum of the reciprocals of each of the three pairs of the same numbers.  I could write it like this if you like:  (1/a)+(1/b)+(1/c) ≥ 2(1/(a+b)+1/(a+c)+1/(b+c))

So long.

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Comets (which are not asteroids by the way. Neither are they meteors for that matter.)

Well well well.
Well well well well well well.
Life is, you know, lifey.  Stuff is happening.  Things exist.

I hate to be boring and just follow the topical topics, but I have been looking at Chury (as we call him) and Rosetta since July last year.  iWin.

Comets are made of ice and dust.

The word “comet” transliterates as “hairy star.”  What?

Anyway, yes.   Comets are made of ice, frozen carbon dioxide and dust.  As they approach the sun, carbon dioxide beneath the surface of the nucleus sublimes and flies away from the comet in a tail.

The ion tail (type I) points directly away from the sun due to solar winds and is blue.  The dust tail (type II) is curved due to the comet’s motion and is pink or white.

The nucleus is typically quite small (Chury’s is 5X10km) and that’s the solid bit you can’t actually see. It is surrounded by a thin atmosphere known as the coma.   Then you have the tails as well.

Ways for comets to “die”:

  • They get flung out of the solar system
  • They burn up entirely (which is what happened to C\2012 ISON)
  • The volatiles burn up, leaving a solid rock centre which is now an asteroid and NOT a comet
  • It collides with another celestial body and breaks up into little pieces (if this happens on Earth, it could turn into a meteor shower, which is NOT a comet)

Well, what else?

They typically have quite short orbits, which are inclined in the what’s-it-called plane that our orbit lies on.  Meh.

They are blob-shaped.  Like a potato, but massive and cold.

Yeah.  I’m bored now.  I’m trying to work out how to use Blender.  It is not what I would call intuitive.

Hmmm… what else is happening in my life?
Not that you would care.
Sherlock happened.  That was cool.  But a while ago now.
I’m a prefect.  Boring.
Somebody started a rumour that I am going out with somebody else.  Very boring.
I learnt how to tie a tie.
I started reading “A Tale of Two Cities.”  That’s quite interesting.
No….  nothing really remarkable.  Ah well.

Until I next have nothing else to do other than blog….
From me

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The Epitome of Repasts

I wouldn’t normally post something like this.  If you must know, it is copied verbatim from a recent piece of homework.  But it is all true, and anyway I think it is rather well written.

So here goes:

With a total lack of expectancy for anything so grand, I allowed myself to be swept over the marble floors, across the wide foyer and up the stately stairs.  We were shown to our seats by an obsequious man in a black suit, who offered to take our coats.  I, intimidated, declined.

Finding it hard to relax amongst so much finery, my attention turned to my surroundings.  The room was overwhelmingly immense, and undivided by walls or screens of any kind.  Indeed, had there been walls enough, it would have made a very comfortable two-storey house.  The lampshades were greatly varied, but uniformly intricate. The walls were blandly white. Through the floor-to-ceiling windows, a magnificent view of the street below was afforded, people scurrying about their daily business, each absorbed in their own universe, and the age-old architecture of the metropolis displayed for us.

As this was a Sunday, the vast array of victuals was laid out in an adjoining room for self-service.  Most of it was, thankfully, recognisable to a certain extent. A plinth stood towards one end of the assemblage, swarming with sumptuous salads.  No doubt they had exotic and elegant names, and would have taken umbrage had they known that to me they were unassumingly “couscous,” “green one,” “one with red onions” and the like.  Scientific curiosity dictated that I sample some of everything, regardless of appearance.  All were exquisite culinary triumphs.

Vegetarian as I am, I was unable to appraise the “impressive carvery selection,” but the “fresh market vegetables and crisp salads,” were delightful enough. The roast vegetables were truly incomparable.  There were potatoes, parsnips and carrots galore, accompanied by splendid Yorkshire puddings, complemented by a brilliant bread sauce and insulted by an unfortunate horseradish sauce.

Finally, the desserts.  Row upon row of heavenly bundles of delectability.  Once more, my innate curiosity whispered its insidious insinuations in my ear, and I found it impossible to desire only one of these fabulous delicacies.  After much deliberation, I opted for an indulgent fruit salad, a paragon of a sweet concoction, and what professed itself to be lavender cake.  I had never partaken of lavender before, and it disconcerted me how precisely similar to the familiar smell the taste transpired to be. However, this novel comestible proved to perfection incarnate.

 

 

May I draw your attention to the word “complement,” which is not to be confused with the word “compliment.”  (Although I did use it as a pun.)  “Complement” means “complete, make up a whole, or bring to perfection,” whereas “compliment” means “express praise, admiration or congratulation.”

On a totally unrelated note, here is a higher resolution version of that quote:

Life... is like a grapefruit.  It's orange and squishy and has a few pips in it, and some folks have half a one for breakfast.

Life. Don’t talk to me about life.

Toodle-pip!

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Utalitarianism

Well.
When I was small (which I still am. A few years ago), I asked my mummy what utilities are. And she told me that they were an imaginary unit of happiness.
I thought that was pretty cool.
And it kind of stopped there.

Until I found out that they weren’t actually imaginary. So here is some stuff about them.

Well, first of all, for any given calculation, you can choose the scale. So if you wanted to know whether or not it would be a good idea to go to war against some evil person who wants to take over the world, then you might assign a utility of 1 to each life that would be lost in each scenario, and anything less significant than death just doesn’t register.

Equally, if you wanted to decide whether or not you should eat the last chocolate biscuit now, or save it for later, then maybe eating it now gets a utility of ten, but you’ll regret it tomorrow when there aren’t any biscuits, so that’s a utility of minus seven, whereas not eating it now, and having it stare at you seductively all day will have a utility of minus nine, but the sweet moment when your mental barriers finally give way, and, unable to resist its overpowering allure, you seize it and devour its flesh in a sudden burst of triumph, submission and savage desire, that will get a utility of sixteen. So overall, eating it now gets a utility of three, and saving it for tomorrow gets a utility of seven. Please forgive me, it’s past my bedtime. By twenty minutes. Golly gosh and goodness me.

Anyway, as you can hopefully see, a utility of one for a life and ten for a biscuit are in no way commensurate, but they are completely isolated problems, and the solutions will not be compared.

Expected utility calculations get complicated sometimes. For example, it is quite obvious that if you robbed a millionaire, and left them with nothing, then gave say £10,000 to 100 people, the overall utility of the transaction would be positive. But people don’t go around doing that, and not out of sympathy for the millionaires. There are decent millionaires out there, certainly. JK Rowling for one. But even if it was somebody who cheated and gambled and trod on people’s toes and backstabbed all their friends and then fed their grandmothers to the Ravenous Bug-Blatter Beast of Traal (it was time. This post was too long to escape without a Hitchiker reference), then you still can’t do that sort of thing, however much you ought. One school of thinking says this is because you should imagine what society would be like if everybody did the same kind of thing for the same kinds of reasons, which us obviously that it wouldn’t be at all safe or stable and people would just sit around waiting to be given bounties from ex-millionaires instead of working. Or perhaps they wouldn’t. Anyway, you don’t do that because it’s far too sensible, and you would rather abide by the rules of normality. After all, they are there to keep you safe. Allegedly.

Anyways,
Rom-halan.

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Relativity

Yeah, well.
I’m still alive. I’ve just been somewhat… distracted.
Anyways, relativity.
And Einstein and stuff.

Einstein is most famous for the equation E=mc^2 (and it still annoys me that I can’t do superscript), even though he himself later found it to be incomplete.
But first, what does it mean?
It means that matter and energy are relative, my friend.
Now, the complete version is: E^2=(mc^2)^2+(pc)^2
The weirdest thing about this? It allows for negative energy, and negative mass. I talked about antimatter once, a long time ago. Negative energy is a different story, with a different protagonist (Dirac, if you were wondering).
But still.
This means that if you could slow a photon down, it would have mass. Weird, huh?
They have managed to stop photons in Bose-Einstein Condensates (BECs), most notably of the element Rubidium.
But I’ve just remembered that I was going to talk about the relativity of space and time, not of matter and energy.

So lets do that instead.
I think we should have a Douglas Adams quote about now-ish. Here’s one: “Just as Einstein observed that space was not an absolute but depended on the observer’s movement in space, and that time was not an absolute, but depended on the observer’s movement in time, so it is now realized that numbers are not absolute, but depend on the observer’s movement in restaurants.”
Here’s another: “The whole fabric of the space-time continuum is not merely curved, it is in fact totally bent.”
I thought we could have two, as it’s been such a long time.
So, if space and time are relative, and depend on your movement through them, it is supposedly true that if one were to travel at the speed of light to somewhere far away, and then come home again at the speed of light, they would not have aged. This is known as the twin paradox. However, as no frame of reference is preferred (by the universe, that is, not me), then how would one know if the twin in the rocket was the one to move so fast they didn’t age, or the one left behind?
According to Copenhagen, this ought to average itself out, similiar to the principle of least action. Have I told you about that? I can’t remember. Never mind.
According to the Multiverse Theory (really called the Many-Worlds Hypothesis, but that’s boring. I personally call it WSOGMM, because I am a Hitchhiker fan), sometimes it would be one, and sometimes the other. According to this hypothesis, we will all get very confused.
But it might be possible to journey to a distant star at nearly-the-speed-of-light, because very little time would pass on the spaceship.
I doubt it, though.

And now, the post is nearly finished.
But I have one more thing to say to you.
At school, my class was told to give an assembly on “all things inspirational” and it was decided that everyone should contribute one slide to the powerpoint. My one was this:

grapefruit1

 

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Boolean Logic

Hiya!
Did you miss me?
I missed you.  A hug without you is just mercury. :P
Anyway, what was I saying?
I don’t know.

This week, I am going to try to learn pi up to the Feynman Point, which is the first place where it goes 999999.
This means I have to learn 762 digits.  So far I’ve got 60-something.
I might stop at 314, as that would also be cool.
All very well, but what was the point of this post?

Ah yes, I am now looking at the title, and can see that I was going to talk about Boolean Logic.
The content will be much the same as in this one, but explicated differently.

So yes.  When asked, “would you like peas or beans with that?”, you should reply either “yes”, or “no”.
This is a good example because you can put brackets in to change the meaning:
-would you like (peas) or (beans with that)?
-would you like (peas or beans) with that?
I do hope you understand the difference.

As ever, there is no real excuse for the delay, but the official explanation is that I’ve got Facebook now.
And, what’s more, someone to talk to on it who I don’t see nearly every day anyway. Bonus!

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An exercise in probability

Yeah, hi.
Sorry again that it’s been a while.
This is just something I thought of and needed to write down in order to think about it at all.

So.
I have three dice, which we will call d1, d2 and d3.
They are all cubes, but two of them are fair, and the other one is loaded to give an even number 2/3 of the time instead of 1/2.
I don’t know which one is loaded, so we assign a 33.3*% prior probability to each one being the loaded one.
To try to find out, we roll each die once.
They all come up four.

So the calculations are:
p(A|B)=p(B|A) * p(A) / p(B)
Or, p(A|B) = 2/9 * 1/3 / 5/27
Which I believe is 2/5, or 40%

Now the catch:
If all the dice have a 40% probability of being loaded, but only one of them is, something must have gone wrong, right? You oughtn’t get a probability sum greater than 100% for mutually exclusive events.

Now, what if we evaluate them all together, at one time?
Instead of B being “we got a four on this particular die”, B will be “we got a four on all the dice”.
Intuitively speaking, this should mean that the calculations are conservative, since it is equally likely that they are all the same regardless of which one is loaded.

So.
p(A|B) = 1/162 * 1/3 /  1/162
Which is, indeed 1/3
Good.

And the moral of that story is: you should focus on the bigger picture, rather than what happened to each individual.

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