I don’t mean to be pedantic, but why do you write “H20” instead of “H2O?”
AnthonyC
If it were revealed to me that, say, the Aztecs were right, their gods are real, and the One True Religion, then I believe it would be my duty to defy their will, and reject their plan for mankind. Power does not grant moral authority, even if it is the power that was used to make the world as it is.
Would I be brave enough to do it in practice? I have no idea, but I think it helps that I’m thinking about it beforehand.
My favorite answer to this problem comes from “How to Cut a Cake: And Other Mathematical Conundrums.” The solution in the book was that “fair” means “no one has cause to complain.” It doesn’t work in the case here, since one party wants to divide the pie unevenly, but if you were trying to make even cuts, it works. The algorithm was:
Make a cut from the center to the edge.
Have one person hold the knife over that cut,
Slowly rotate the knife (or the pie) at, say, a few degrees per second.
At any time, any person (including the one holding the knife) can say “cut.” A cut is made there, and the speaker gets the thus-cut piece.
At the end, anyone who thinks they got too little (meaning, someone else got too much) could have said “cut” before that other person’s cut got too big.
“”If I had not done among them the works which none other man did, they had not had sin: but now have they both seen and hated both me and my Father”
Even the Bible doesn’t demand blind faith.
I agree about the usefulness of a basic technical understanding of as many fields as possible. As for the push to specialize in academia- well, it’s complicated. I’m not a professor, I’m a grad student, but here’s my experience. If you’re in one of the relatively “pure” discipline- physics, computer science, and so on- the push to specialize is very real, as is the push to focus on what everyone else (including granting agencies) thinks is “hot.” But there is a lot of multi-disciplinary work going on, an increasing amount really. Trouble is, that quickly becomes a new discipline in its own right. My alma mater now has 5 different biology majors, each of them interdisciplinary in interesting ways. My own field- materials science- encompasses the study of solids and liquids. Metals, alloys, ceramics, oxides, semiconductors, polymers, and even biological materials. It can’t be done unless you understand organic and inorganic chemistry, crystallography (applied group theory, really), physics (classical- strain fields, shearing forces; and quantum- bloch waves, electronic band structure), and enough computer science to right some basic simulations. You end up with professors working in fields that didn’t exist when they started out. So they keep taking classes and reading each other’s books.
Consider the set of all possible hypotheses. This is a countable set, assuming I express hypotheses in natural language. It is potentially infinite as well, though in practice a finite mind cannot accomodate infintely-long hypotheses. To each hypothesis, I can try to assign a probability, on the basis of available evidence. These probabilities will be between zero and one. What is the probability that a rational mind will assign at least one hypothesis the status of absolute certainty? Either this is one (there is definitely such a hypothesis), or zero (there is definitely not such a hypothesis, which cannot be, because the hypothesis “there is definitely not such a hypothesis” is then a counterexample), or somewhere in between (there may be, somewhere, a hypothesis that a rational mind would regard as being absolutely certain). So I cannot accept your hypothesis that there does not exist, anywhere, ever, a hypothesis that I should regard as being absolutely certain.
There is, of course, also the observation that on Feynmann diagrams, positrons behave like electrons moving backwards in time, whatever that means. This suggests a hypothesis that, perhaps, there is only one electron, moving forward and backward in time, interacting with itself...
“You’d think they’d tell you up front, “Hey, the evolution of a quantum system depends on stuff like the second derivative of the amplitude distribution, so you can’t possibly break it down into the evolution of individual configurations.” It’s worse than that; they wait until the 2nd semester to even start talking about time-evolution. They spend the first semester trying to find, for a given Hamiltonian, a set of wavefunctions for which the value of a particular observable, energy (or in a few cases, momentum), is unchanging in time. Time-evolution is presented only as a consequence of either a superposition of time-independent states, or as a changing external potential. Which really misses the point: the “superposition” is already a valid solution to the full schrodinger equation in it’s own right, and the whole concept of an external potential is a result of our inability to account for each particle in the system at once.
“How fast does the little arrow rotate? As fast as the photon’s wavelength—that’s what a photon’s wavelength is. The wavelength of yellow light is ~570 nanometers: If yellow light travels an extra 570 nanometers, its little arrow will turn all the way around and end up back where it started.”
Which would seem to make it a ruler as well as a clock. But then, since general relativity made time an axis like space, I have sometimes wondered why we don’t measure time in meters or distance in seconds.
In light of this, consider the cosmologist’s claim that the total energy of the universe- rest-mass plus kinetic plus all the fields, especially gravitational, could very well turn out to be zero. Then your entropic formulation here could suggest a plausible answer to “Why is there something rather than nothing?” and “Why did the entropy of the universe used to be so low?” If, initially there was nothing, it takes no information to specify the universe’s state. Minimum entropy. The spontaneous introduction of particles (with no net energy change) represents an increase in entropy. The process by which that initial state would rise in entropy is still ongoing, just as a hot object takes finite time to reach equilibrium with it’s surroundings. In the case of a star that process can take trillions of years.
Say I start with an amplitude distribution- essentially an n (potentially infinite) dimensional configuration space with a complex numbered value at each point.
This is essentially an infinite set of (n+2)tuplets. If I knew the dimensionality of the configuration space, I could also determine the cardinality of the set of n+2-tuplets for a particular distribution, as well as that of the set of all possible such sets of n+2-tuplets. (Unless, of course, one of these collections turns out to be pathologically large, hence not a set, but I don’t know why that should be).
Then it would seem that I can represent a quantum amplitude distribution as a single point moving around in a configuration space- albeit a much, much larger one.
could the flow of amplitude between blobs we normally think of as separated following a measurement possibly explain the quantum field theory prediction/phenomenon of vacuum fluctuations?
Your decision to try and learn to become more rational already demonstrates that you are not average.
Try to learn as much as you can, about as many fields of inquiry as you can, including probability.
Someone needs to teach them how to count: {}, {{}}, {{},{{}}}, {{},{{}},{{},{{}}}}...
VII-IX actually did get into the expanded universe, but, AFAIK, only as comics, not novels.
And, in fact, the emperor returns from the grave by possessing clones he had made in advance. He turns Luke to the dark side, and Leia turns him back, and together they destroy the emperor.
Not that that affects this post one iota, just a tangent.
Is this a problem prevalent in computer science generally, moreso than other disciplines? Lots of companies, for example, think they can write their fancy software suite in six months, without designing it in detail first, and still be working on it five years later. OTOH, the physicists, chemists, and in some cases engineers seem to have no problem saying “we have no idea how this phenomena works. It’s going to take a lot of people and a lot of time and a lot of money to develop understanding and control of the process.” That, of course, could just be a side effect being graded on publications and grants rather than products, but it’s still suggestive.
Socrates definitely drew on some questionable intuitions in Plato’s dialogues, but I think justice is a particularly slippery concept, in that it requires a prior conception of both the law and the good.
Legality is, for any sufficiently well-written laws, a purely factual matter. Does x break the law? Yes/no. Morality is, for any particular sufficiently well-written moral system, also a factual matter, but with more degrees of freedom. Is x good? Is x optimally good? Is x bad, but the best available option? Is the moral law, as written, itself good or optimally good under it’s own definition of goodness?
Justice flings this all together in one pot: What ought the law to be? How ought the law to be enforced? How should we feel about the execution of justice?
This may be relatively clear to most readers of this site who grew up aware that good/evil and law/chaos are largely orthogonal, but in my experience many (most?) people have significant confusion/crossover between “illegal” and “immoral.”
We are among (aka “with” aka “con-”) those those who have read the Sequences, so maybe… Consequentialists?
Oops, already taken.
About your grandparent’s house: i seems to me like once you specify the probability of renting and selling at 40% and 15%, you have already decided that the probability of neither happening would be 1-(1-.4)(1-.15)=49%. This appears inconsistent with the 45% prediction, or am I missing something?
“Even if you try to have a chain of should stretching into the infinite future—a trick I’ve yet to see anyone try to pull, by the way, though I may be only ignorant of the breadths of human folly”
I thought this was a part of the principle of utility. Happiness today is no more inherently valuable than happiness tomorrow. The consequences of an action, and the utility associated with those consequences, ripple forever throughout time and space, far beyond the ability of my finite mind to predict and account for.
At least, that thought is what led me to decide that “I can accept this principle as true, but it isn’t often going to be useful for making decisions.”