The legomenon blog

November 6, 2008

The first Hawaiian president of the United States

Filed under: Politics — legomenon @ 10:02 am

A person is either born in Hawaii or not born in Hawaii. Except for extremely pathological borderline cases, you can’t be born just a little bit in Hawaii. But you can be a little bit “black” and a little bit “white” if you have mixed descent. Barack Hussein Obama II has such mixed descent: black father, white mother. So why is he always labeled “black” and never “white”? And if his heritage is so important, why is his hawaiian background so seldom mentioned in the media?

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August 3, 2008

It’s not too late for a boycott

Filed under: Politics — legomenon @ 10:03 pm

This upcoming friday, the 2008 Summer Olympics will be officially opened. This will be a huge propaganda victory for the chinese government. Not for the legal democratically elected chinese government in Taiwan of course, but for the bandits in Beijing who control mainland China, Tibet, and parts of Ladakh.

Proponents of the Beijing Olympics assured the world seven years ago that the human rights situation was improving in China, and that everything would be all right by 2008. Awarding the games to the communist regime was even supposed to “help” this to happen. This was an irresponsible lie even back in 2001, propagated by people who should have known better. Of course the communists will always continue to disrespect human rights, simply because at the very moment that they are removed from power via a democratic election, they will be held responsible for their past actions. And when you know you are a bandit, this is the last thing you want to happen.

But the rest of the world can still make a difference. Athletes: don’t go to Beijing. Make a stand, even if it’s the only time you ever make a political stand in your entire life. People everywhere: make a note of the companies that are official sponsors, and stop buying their products. Sell any shares that you own in these companies. You can always buy them back later at a lower price 🙂

And don’t forget to tell everyone why you are doing this.

And a personal note to Mr. Dalai Lama the 14th: I very much appreciate and agree with your total commitment to a non-violence policy. But you are doing a disservice to your people by not demanding full sovereignty for your country. And please do whatever you can to stop all this superstitious reincarnation bullshit. This is truly opium for the people, and an obstacle for anyone interested in spiritual liberation.

July 13, 2008

Why three space dimensions are necessary for sight

Filed under: Philosophy — legomenon @ 6:26 pm

John Wheeler is reported to have said:

Time is what prevents everything from happening at once.
Space is what prevents everything from happening to me.

I won’t address the dimensionality of time here, I’ll save that for a later post maybe. Let me just briefly remark that I think the observation that time is 1-dimensional is a consequence of the fact that only a 1-dimensional time makes it possible for different observers to share an objective reality where causality is possible. So let’s stick with one single time dimension, and consider space and how it’s possible to see things at a distance.

In order to see things clearly at a distance, it must be possible to transport light signals across space with little or no distortion. Since light is a type of electromagnetic wave, the propagation of waves must allow such transporting of signals. The wave equation in n-dimensional space looks like this:

\displaystyle \frac{\partial^{2}\psi}{\partial x_1^{2}} + \frac{\partial^{2}\psi}{\partial x_2^{2}} + \dotsb + \frac{\partial^{2}\psi}{\partial x_n^{2}} = \frac{1}{c^2}\frac{\partial^{2}\psi}{\partial t^2}

where c is the propagation speed of the waves, and \psi represents the stuff that is “waving”, whatever it is. More precisely, \psi is a function of space and time coordinates, and the value of that function can be any mathematical object for which partial derivatives are defined: for example a simple scalar, a complex number or quaternion, a vector, a matrix, and a lot of other things.

Now imagine a wave that propagates from a point-like source, symmetrically in all directions. The symmetry allows us to write the wave equation in terms of only r and t, where r is the distance from the source. This spherically symmetric wave equation looks like this:

\displaystyle \frac{\partial^{2}\psi}{\partial r^{2}} + \left(\frac{n-1}{r}\right)\frac{\partial\psi}{\partial r} = \frac{1}{c^2}\frac{\partial^{2}\psi}{\partial t^2}

In order to transport an arbitrary signal, the wave function must hold for all solutions of the form

\displaystyle \psi = f(r-ct) \gamma(r)

where f is an arbitrary function that represents the shape of the source signal, and \gamma is some fixed function that is independent of f. The factor \gamma(r) attenuates the signal as it spreads outward from the source. Since the wave equation must hold for any f, it must in particular hold for the case f \equiv 1, which gives the condition:

\displaystyle \frac{\partial^{2}\gamma}{\partial r^{2}} + \left(\frac{n-1}{r}\right)\frac{\partial\gamma}{\partial r} = 0

which, ignoring irrelevant constants and the pathological case n=1, has the solution

\displaystyle \gamma(r) = \frac{1}{r^{n-2}}

which gives us \displaystyle \psi = \frac{f(r-ct)}{r^{n-2}} for the general case, since \gamma is independent of f.

Inserting this into the spherically symmetric wave equation produces, after simplifications,

\displaystyle \frac{f''}{r^{n-2}} - 2\left(\frac{n-2}{r^{n-1}}\right)f' + \left(\frac{n-1}{r^{n-1}}\right)f' = \frac{f''}{r^{n-2}}

where f' and f'' are the first and second derivates of the function f with respect to its parameter. After further simplification the final result is simply n=3. Voila! So faithful propagation of arbitrary signals via spherically symmetric waves is only possible in 3 space dimensions.

Notes:

‱ I only bothered with so-called “retarded” waves. Since the wave equation only uses the second derivative with respect to t, any linear combination with a solution that uses -c instead of c is also a solution. Solutions of the form f(r+ct) are called “advanced” waves and are the time-inverse of the normal retarded solutions.

‱ Spherical symmetry is an idealization for electromagnetic waves, since the electric and magnetic fields (or the Faraday tensor if you prefer) have directions in space which are transverse to the direction of wave propagation. See The Hairy Ball Theorem. This doesn’t affect our conclusion, however.

‱ There are some speculative exotic theories (string theory etc) that postulate several extra “compact” space dimensions in addition to the familiar ones that we already know about. This does not affect our conclusion either, since such hypothetical dimensions do not contribute to any degrees of freedom in a macroscopical wave equation.

July 11, 2008

Anton Nilson – a swedish terrorist

Filed under: Politics — legomenon @ 5:12 pm

Today, or rather tonight, marks the 100-year anniversary of one of the most famous terrorist attacks in Sweden, the bombing of the ship Amalthea, which resulted in the murder of Walter Close, and the maiming and wounding of several other civilians. The person responsible for this horrible act of violence was Anton Nilson, but the blame also falls on his fellow collaborators Algot Rosberg and Alfred Stern. All three were communists, and this case is of course just one more example among many that shows how communism always perverts the last vestiges of morality within the ranks of its believers.

The perpetrator Anton Nilson emigrated to the Soviet Union after he was released from prison, and spent a decade participating in Lenin’s Red Terror against liberals, social democrats, anarchists, and anyone else who didn’t submit to Lenin’s totalitarian rule.

All this happened a 100 years ago, but some people still refuse to learn the lesson that communism is pure evil. Two influential swedish social democrats Olof Palme and Ingvar Carlsson, both who served as prime ministers of Sweden, actually celebrated the terrorist Anton Nilson on various occasions. Maybe they didn’t know who Anton Nilson was, and the crimes he committed. Or maybe they did? Either way it’s very very scary to know that such blood-thirsty people have actually led governments in my country.

July 2, 2008

FRA-lagen

Filed under: Svensk Politik — legomenon @ 8:23 pm

Nu har det gĂ„tt tvĂ„ veckor sedan “Lex Orwell” klubbades igenom i den svenska riksdagen. Trots en massiv kritik frĂ„n mĂ„nga svenska medborgare som Ă€r vĂ€l införstĂ„dda med hur Internet fungerar, vad syftet med den svenska grundlagen Ă€r, och som kan kĂ€nna igen en lobbyistisk “Spin Doctor” pĂ„ 1000 kilometers avstĂ„nd, sĂ„ Ă€r argumenten hos FRA-lagens föresprĂ„kare fortfarande begrĂ€nsade till: (1) BuĂ€hÀÀhÀÀÀ!!!! Mina vĂ€ljare förstĂ„r mig inte! (2) Yttre hot… i framtiden kanske… men tĂ€nk pĂ„ vĂ„ra svenska barnsoldater som krigar i Afghanistan! samt (3) Andra vĂ€rldskriget minsann!.

Sedan har det dykt upp ett antal Äterkommande begrepp i debatten som jag tror det Àr nyttigt att skÀrskÄda:

  • “Teknikneutral” betyder att man istĂ€llet för att bara spana pĂ„ radiosignaler som avsĂ€ndaren har sĂ€nt ut för spridning överallt i etern, vill kunna spana pĂ„ alla meddelanden som skickas överhuvudtaget, oavsett teknik. Det tycker jag Ă€r helt OK sĂ„ lĂ€nge samma grundförutsĂ€ttningar gĂ€ller som tidigare: FRA bör fĂ„ spana pĂ„ allt som sĂ€nds via kabel och som sprids överallt, d.v.s. all annonserad multicast (RFC1112 m.fl.), allt som skrivs pĂ„ publika websajter, och Ă€ven allt som Ă€r allmĂ€nt Ă„tkomligt via FTP och Bittorrent naturligtvis. För detta krĂ€vs ingen massiv avlyssningsapparatur. Det rĂ€cker med en vanlig internetanslutning. Med FRA:s budget sĂ„ skulle dom kunna köpa sig en miljon vanliga internetanslutningar. Om jag var FRA-chef sĂ„ Ă€r det precis vad jag skulle göra.
  • “Kontrollstation” betyder i praktiken att regeringen och FRA sjĂ€lva ska utvĂ€rdera i efterhand huruvida regeringen och FRA har missbrukat sina befogenheter. HallĂ„?
  • “Integritet” betyder pĂ„ FRA-lobbyisternas nysprĂ„k att FRA först öppnar ditt brev, tar en kopia pĂ„ det, granskar kopian maskinellt, sparar information om innehĂ„ll och metadata, och till sist “förstör” den sparade informationen efter att ha lĂ€st och tolkat den och konstaterat att den för nĂ€rvarande inte Ă€r intressant för FRA:s kunder.

Jag kanske ska pÄpeka att jag inte Àr principiellt mot avlyssning av kabeltrafik. Det finns situationer dÀr detta Àr befogat och önskvÀrt. Men det Àr en stor skillnad mot FRA-lagens massavlyssning av alla. Och det kom som en kalldusch för mig att hela den borgerliga alliansen (med undantag för riksdagsledamot Camilla Lindberg) accepterade massavlyssningen. Jag har röstat anti-socialistiskt i alla val jag har deltagit i, men frÄn och med FRA-lagen kan jag inte lÀngre rösta pÄ nÄgot av allianspartierna. Att rösta för ett visst parti innebÀr att man som individ legitimerar dess politik, och dÀrför Àr det helt uteslutet för mig att nÄgonsin mer rösta för nÄgot av de partier som klubbade igenom denna lag.

June 30, 2008

The whole vs. the sum of its parts

Filed under: Philosophy — legomenon @ 6:28 pm

If you disassemble the engine of your car and put all the parts in any random order in a pile on the ground, it will be obvious that a car engine is much more than just a collection of parts. If this isn’t obvious, do the disassembly experiment and then turn the ignition key and see what happens.

That is not what this post is about, though. Instead I want to point out the difference between sums and sums, or rather the confusions that occur due to the different interpretations that can be applied to the word “sum”.

An arithmetic expression like 1+23+99+42 is typically called a “sum”. But “the sum” of the numbers in that expression is 165 which is a number, not an expression. The expression 1+23+99+42 has distinct parts: these parts are the numbers 1, 23, 42, 99, and the operators that connect those numbers. The sum 165 on the other hand is just one single part all by itself. Or perhaps it consists of 165 parts which are all copies of the number “1”. Or perhaps it consists of the prime factors 3, 5, and 11 multiplied together. The possibilities are endless, and it doesn’t really matter since all these “perhapses” refer to implicit structure, not to anything explicit in the original expression.

The resulting confusion is entirely semantic. When we say “2+2 = 4” we only mean that 2+2 and 4 have values that are identical, not that the expressions themselves are identical. They can’t be identical since the expressions have different structure. Things that are identical can’t have any properties that are non-identical (cf. Leibniz’ law).

The same confusion reappears in many other contexts. One example is “the will of the people”, which is a straight-forward concept when it refers to a collection of varying individual preferences, but it’s something completely different when it refers to a single collectively held preference. The latter is not even well-defined in the general case, due to a mathematical result in social choice theory known as Arrow’s theorem. This has far-reaching consequences for politics and ethics.

June 29, 2008

Hello world!

Filed under: Uncategorized — legomenon @ 6:24 pm

From early experiments with written notes, bottle messages, snail mail, dial-up bulletin boards, e-mail, usenet, hand-written web pages, internet relay chat, web forums, and wiki, I have now belatedly reached the blogosphere. Let’s see how this thing works.

((e^{\pi})^{2})^{\sqrt{-1}} = 1

Having built-in Latex support is nice! 🙂

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