Interstellar 2 – Impact

The first posting in this series explained how immense the interstellar distances are, and how, as a consequence, any spacecraft would have to travel at a very high speed to get even to our nearest star system in a reasonable length of time, say a century or less. But at such a high speed, hitting even the tiniest dust particle could be disastrous. Let’s explore that.

Interstellar space is very empty, a more complete vacuum than is typically achieved on earth in a vacuum chamber. But interstellar space is not completely empty – it contains a very thin mixture of gases and small dust particles, and very occasionally something larger. We see those occasional larger items as “shooting stars” at night when they burn up in our atmosphere.  So anything traveling at high speed through interstellar space for many decades is bound to occasionally run into something, even if it is only a tiny dust particle.

Now since the speeds involved are a significant fraction of the speed of light, relativistic effects begin to appear. Masses increase as we approach the speed of light, though at only 10% the speed of light the change is less than 1%, so we can ignore it and use the standard Newtonian  equation for the kinetic energy of an object, which is K.E. = ½ m v², or kinetic energy is half the mass times the velocity squared. It’s that last term that is the problem for us, the velocity squared. At, say, 10% the speed of light our velocity is already immense, and then we square it!!

And that assumes the particle we run into is standing still relative to us – if it is coming toward us its speed is added to ours in that last term squared!!

So lets put some actual numbers to this, to see what the implications are.

Estimates are that most interstellar dust particles have a mass somewhere between 10^-16 kg (0.1 pg.) and 10^-4 kg (100 mg.).  A standard-size paper clip weighs about 1 gram, so let’s assume a tiny dust grain 1/100 of the size of a paper clip, or 1 mg.  And let’s assume we are travelling at 10% the speed of light, or about 30,000 km/sec. Then the kinetic energy at impact of this little dust particle on our little space probe is about 4,500,000,720 Joules.

How much is that (for those who don’t typically think of the world in terms of Joules)?  Well, if we fired a typical 180 grain bullet at our space probe from a .357 magnum handgun, it would deliver about 720 Joules of energy, and no doubt thoroughly wreck the space probe. But at 10% the speed of light, impacting our little 1 mg dust particle will do over 6 million times more damage!

If our little interstellar probe is going to survive a century-long trip to Alpha Centauri, it is going to need a massive shield in front of it to protect it from such impacts, and the mass of that shield will have to be accelerated along with the rest of the probe, at an enormous cost in energy. So that is problem number 2.

 

Federal power

Recent Supreme Court decisions have, predictably, produced a lot of angry but largely uninformed reactions among the politically polarized media and activists on both sides of the political fence. I wouldn’t presume to know what is really in the private minds of each of the justices (a restraint not shared by some in the media), but can only judge them on their writings and decisions. It seems to me, if one ignores the emotional and political baggage around some of these rulings, that there is a clear thread in those decisions, and it is the issue of federalism.

The nation was founded as a federation of states, states who were reluctant to give up any more sovereignty to a central government than was absolutely necessary to hold the nation together and provide for effective common security against outside invaders. They had tried before, with the Articles of Confederation written in 1777 and finally ratified by all the states in 1781, but that document proved to be too weak to do the job, so they tried again at the Constitutional Convention of 1787, producing the constitution we currently have, which divided power between the individual states and a central federal government whose powers were fairly limited.

In the intervening decades there has been a natural tendency for the central government to grow in size, become more bureaucratic, and attempt to aggregate to itself more power over the states. The exigencies of World War II accelerated this trend toward more centralized power. In parallel with this, within the federal government itself each of the three branches have also pursued a natural bureaucratic tendency to try to grow their power over the other two. Thus the Supreme Court in Marbury v. Madison (1803) arrogated to itself the power to rule on the constitutionality of laws passed by Congress, a power not given them in the constitution. And in recent decades the Presidency has arrogated to itself powers constitutionally reserved to the Congress, which is why we have had a bunch of wars recently with no Congressional declarations of war, as required by the constitution.

Now a federated system has its strengths and its weaknesses. Having 50 states largely free to try different experiments certainly speeds the process of evolving new ways of solving social and political problems. For example, Alaska’s current experiment of trying ranked-choice voting in an attempt to reduce the partisan divide and force candidates to focus on serving those outside of their natural political base is interesting. It may work, or it may not. If it does, other states may adopt it. If not, it was worth the experiment.

In addition, we are a very large nation, or really 7 or 9 or 11 different nations, according to some authors. Californians have different problems, different values, and different issues than Iowans, Rural Montana faces different conditions than urban New York or rust-belt Michigan. The advantage of a federated system is that if one doesn’t like the policies (say the high taxes, or high home prices, or poor educational system, or the poor social network) of one state, one can vote with their feet and move to another state, which is what is happening currently, for example, with the exodus of people and businesses from high-tax, highly-regulated California to low-tax, lightly-regulated Texas, or the new exodus of remote workers from expensive big cities to less expensive suburbs in other states.

So I would argue that the real split in the Supreme Court in recent decades is not a political one between liberals and conservatives, though that is the narrative the media likes to push. The real split, I would assert, is between those justices who want to increase the power of the central government over the states, moving us from a federated system of states to a more European unitary system, and those who want to preserve the state’s power in a federated system, and even perhaps reverse the growing power of the federal government.

The majority opinion by the so-called “conservative” justices in recent cases have pretty much favored returning power to the states, and limiting the power of the federal government. The recent vaccine mandate ruling, which prohibited a federal government agency (OSHA) from requiring all large employers across the nation to force all their workers to get vaccinated, is one recent example. If Roe v. Wade is overturned, it will be on the basis that individual states, not a central government (and certainly not an unelected judiciary) ought to decide that moral question for themselves, presumably based on the majority moral position of the inhabitants of each state.

The current battle in Congress to pass a “voting rights” bill is essentially a move to take away from the states the power to set and administer their own election laws, a power reserved to them in the election clause (Article 1, section 4) of the Constitution, though with the proviso that Congress may alter those regulation by law.

The so-called “liberal” justices, on the other hand, have voted consistently to give the central government more power to impose and enforce a common position (generally a “liberal” position) on the entire population of the nation.

Clearly this is a difficult issue. The federated system has its problems. States have in the past adopted regulations and positions antithetical to the fundamental premises of the constitution. Slavery and subsequent segregation laws are the prime examples but by no means the only ones.  

On the other hand, the flexibility and dynamism of 50 states “competing” with one another for population, labor and businesses has certainly proved more successful than the “central planning” model of unitary European and Asian systems. And in a nation as large and diverse as ours, heavily bureaucratic “one-size-fits-all” regulations from a central government tend to be inefficient.

This is a matter of balance. Opinions naturally differ about where the balance between state power and federal power ought to be. But a rational discussion about this balance of power would probably be far more fruitful than the emotional and largely irrational “liberal” versus “conservative” Supreme Court narrative pushed by the media.  

 

Incerto 6

Another nugget from Nassim Taleb’s Incerto series of books. In his book The Black Swan, Taleb discusses what he called the ludic fallacy (ludic from the Latin ludus – games).  In essence the ludic fallacy is to believe that real-life events are statistically as simple as games of chance in a casino, and can be predicted as accurately.

In a casino (an honest one, that is) the rules of the games are fixed and clearly stated, and so probabilities can be computed accurately. (Honest) dice always have six sides and are not loaded. (Honest) coins have equal odds of heads or trails. (Honest) roulette wheels have no magnets, so the chances of the ball entering any given bucket are equal, and so on.

In real life, metaphorically, the dice may be loaded, the coin may well be biased, the rules may change unpredictably, and the roulette wheel may well have magnets. Classical statistics is based on the properties of the Gaussian distribution (the Bell curve) with some strong assumptions (observations are independent, and path independent, etc). In games we know the characteristics of the generator (eg – the dice, or the coin, or the roulette wheel).  In real-life events the generator is usually very complex, often largely invisible (often including the actions, agendas, decisions, and complex motivations of many people), and often (or perhaps usually) includes random elements. Most games of chance are in the domain of “Mediocristan” where there are few outliers more than 3 standard deviations from the mean; many real-life events are in the domain of  “Extremistan” where the distribution may be “fat tailed”, and where there are  outliers with very significant impacts, represented by decidedly non-Gaussian distributions.

The ludic fallacy is to assume one can apply the simplified games models to massively complex   real-world events. Lots of professional risk managers apparently try to do this, providing ample opportunities for wildly expensive black swans (like the 2008 financial crisis).

In the Incerto series Taleb gives us the non-mathematical logical argument for this. In his massive 455-page technical supplement to the Incerto series, Statistical Consequences of Fat Tails: Real World Preasymtotics, Epistemology, and Applications (which you can buy from Amazon or download as a pdf free from his website here) one can find the rigorous mathematical exposition of his claims.   

Interstellar 1 – Distance

Science fiction movies and books have given the general public the impression that interstellar travel is possible, inevitable, and perhaps even relatively easy. And recent tentative steps to explore the moon, Mars and other nearby celestial objects has reinforced that impression.  But in fact interstellar travel involves some immense problems, and may well be unattainable unless we have badly misunderstood the physics of the universe (always a possibility).

In this short series of “Interstellar” posts I will explore the major problems that would face such an endeavor.

The first problem is the immense distances involved. Our nearest star (actually three stars orbiting each other) is Alpha Centauri, about 4.4 light years away from us.  Now 4.4 is a smallish number, easily graspable by the human mind, but a light year is an immense number, 5.88 TRILLION miles (9.46 TRILLION kilometers).  We humans have trouble getting a “gut feeling” for how far 100 miles is, let alone a TRILLION miles. In fact, we really can’t grasp a trillion of anything except as an abstract number (like the immense US national debt at about $30 trillion dollars).

The fastest spacecraft the world has managed to launch thus far are the two Helios Solar Probes, which were sent near the sun. At closest approach, accelerated by the immense gravitational pull of the sun, the fastest reached a speed of about 250,000 km per hour. Even at that speed, it would take 18,000 years – longer than recorded human history – to reach our nearest star system, Alpha Centauri.

Clearly any project that took 18,000 years to reach completion would have long since been forgotten or relegated to the realm of myth. So for practical purposes one would need to reach Alpha Centauri in much less time, say in a century or less, and even that would stretch political and public support, and memory, pretty far.

But to reach even our nearest star system in a century would require traveling an average of at least 10% the speed of light, about 30,000 km/sec. (108,000,000 km/hour), or over 430 times faster than any spacecraft we have ever launched thus far, and that one cheated by using the sun’s immense pull to speed it up. The fasted spacecraft we ourselves have accelerated (without a gravitational assist from the sun) to date is the Voyager 1, headed out to interstellar space about 1/18,000 the speed of light.

So the immense distances involved are our first major problem.