why does the electron field have inertial mass? if it's just bubbles and waves like the em field, why can't it travel the speed of light? is it because it sheds energy to the em field whenever it's moving?

what parts of the em field are quantized? just the values at any given point? the local extrema? the amplitudes of the fourier transform?

how can two fields interact with one another?

in the copenhagen interpretation, how are measurements defined? why don't the two slits collapse the wave, and why doesn't the measuring device cause interference?

why is the weak force considered a force, and not just a collection of interactions? it doesn't really impart much momentum, it interacts mainly through particles rather than fields, it doesn't really have its own associated property (like charge, gravitational mass, etc), and its force carrying particles have mass.

how does the pauli exclusion principle work on electrons that aren't surrounding an atom? does it have some radius of effect? how does it work when you think of electrons as field bubbles rather than particles?

12-11-2017, 01:17 AM(This post was last modified: 12-12-2017, 08:42 PM by a52.)

the multiplicative group over the positive rational numbers is just the direct group product of infinitely many multiplicative groups of powers of some (essentially arbitrary) prime. until you include addition, no one prime can be said to be bigger than another, the "value" of each prime is completely arbitrary/even meaningless, and you can add or remove primes freely without inducing holes.

for example:

the powers of two under multiplication/division are a closed group -- if you multiply any one of them by any other you will end up with another power of two. so, since we always know our number will look like 2^x, let's just drop the 2^, and write (x). now, (x) * (y) = 2^x * 2^y = 2^(x + y) = (x + y). so we can redefine the product operation (x) * (y) as just (x+y).

but wait a minute. if all we have now is the operation (x) * (y) = (x + y), there's absolutely nothing in there forcing the power at the bottom to be two. it might as well be "apples", for all we know or care.

and, as an experiment, what happens when we let every number have two values, instead of just one? let's define (x, y) * (z, w) = (x + z, y + w). what we have now is a multiplication system with two primes. we've come up with a way to represent all composite numbers with these two primes as their only prime factors, as a function of the number of each prime factor in a number. but we don't know what factors are. maybe (x, y) = 2^x * 3^y, but it could just as easily be apples and oranges because we don't actually know what those two primes are, and the two columns never interact in any way, it's meaningless to talk about which is "bigger", and how they are ordered within the number system.

in conclusion:

all the weirdness with primes isn't really anything to do with primes themselves, it only comes about when you combine addition with an infinite-prime multiplicative group. and interestingly, the rules for addition seem very similar to the rules for a single-prime multiplication group.

04-23-2018, 06:23 PM(This post was last modified: 04-23-2018, 06:27 PM by a52.)

In a programming language where the only operations are boolean OR and boolean NOT, all variables are 1-bit, and data can only be read once before it is destroyed, what operations are possible, and how can we distinguish those that are and those that aren't?

Or, if we represent all boolean operations as directed graphs, what operations are both planar and acyclic?

Or, what operations can we make with redstone in minecraft without ever making bridges?

Given some finite collection of positive integers S = {a_{1}, ... } (repeats are allowed) of size N, where you're allowed to ask for the closest number X to some number Y that can be made as a sum of the elements, how many times do you have to ask before you know the whole collection, as a function of N?

For example, if you have the collection {2, 2, 10}, you can determine the set in four guesses, if you somehow know to ask exactly the right numbers. First, ask for the closest sum to infinity, which tells you 14 is the sum of all elements. Your guess for the set is currently {14}. Next, ask for the closest sum to 12, which returns 12. Your guess for the set is now {2, 12}. Next, ask for the closest number to 10. Your guess for the set is now {2, 2, 10}. Finally, ask for the closest number to 7, which gives 10. The only number less than ten that is further from 7 than 10 is 4. 4 cannot be in the set, as to get a total sum of 14, you would also have to have a 6 (or some combination of numbers that add to six) which is impossible, as you already know the closest number/sum to 7 in the set is 10.

In other words, how many different attempted withdrawals from an atm do you have to make to determine what bills are in the atm?

What are the average minimal values as a function of N? The average average values from some algorithm? The average average values from guessing randomly?

05-04-2018, 08:07 AM(This post was last modified: 05-04-2018, 08:08 AM by a52.)

a52 Wrote:atm puzzle

somebody on reddit posted the impossible counterexample of distinguishing {1,1,1} and {1,2}. so i guess im not getting into the next martin gardner book

im sure there's a very simple explanation behind this but im far too tired to figure it out

why do europeans and middle easterns and indians some africans have pointy noises while asians and other africans have flat round ones and why do native americans have pointy noses when they come from asians who have round ones

why do mammals have five toefingers per paw

why do humans laugh and why do we bare our teeth to show nonaggression

could i still sit down if i had a tail

what color were dinosaurs

why do humans assign human attributes, particularly infantile ones, to animals we should be killing and eating? are we really just that social

for that matter, are nonsocial animals capable of feeling empathy/wanting to help somebody that is not them or maybe not even in their species

why is it really easy to fall asleep sometimes and really hard others even when im just as tired

why are plants green instead of black

is oxygen really the best gas for life to live on

we're really lucky that the universal solvent just so happened to be the most likely product of some of the most common elements in the universe

how come gravity doesn't reduce entropy? are gravitational waves kinda like heat is to electromagnetism? would gravity reduce entropy if it was just newtonian instead of gr?

how come when youre really tired and about to fall asleep all of a sudden everything completely loses its sense of scale and everything seems really small and really big and skinny and fat all at once

why don't more people ask more questions there are so many good ones to ask

compare a deinonychus to a wolf, two animals with similar predation patterns that occupy(ed) similar niches in their ecosystem. now compare their skulls. look how much more brain room the wolf has! the deinonychus looks like just a big mouth in comparison. then compare geckos and mice. crocodiles and jaguars. velociraptors and housecats. elephants and triceratops.

Most people would accept that a computer is Turing-complete -- ignoring the fact that a truly Turing-complete machine has infinite memory while (most) of our computers don't. Most people would also accept that something is Turing-complete if it can simulate something that is already Turing-complete.

Is an infinite bag of electronics parts -- wires, resistors, capacitors, inductors, transistors, and diodes -- Turing-complete, then? You can compute anything with them, including a computer, and oftentimes you can make a much more efficient computation machine by building it with electronics rather than by building it with a computer then programming the computer.

The issue is that putting in the input feels an awful lot like building the machine, rather than just telling it what you want to compute. Are the collection of parts or the electromagnetic field really computing anything?

What about a 20 kiloton pile of iron, copper, and various rare earth metal ores? You can make electronics parts from that. But this seems an awful lot less like "simulating" something, and an awful lot more like just "making" it.

What about a single wooden block? You can probably carve something Turing-complete out of wood if you have a good enough chisel.

At each of these examples (it seems intuitive that) less and less computing power is actually present in our "computer" and more and more computing power and work is put into configuring the "inputs" and interpreting the "outputs". Clearly, we have to include other information about the system in the part we consider Turing-complete, probably including the method of adding inputs and instructions on interpreting outputs.

But at what point could we just take the input and output system alone, replacing our "Turing machine" with some arbitrary object? And at what point do we consider the human integral to the operation of our machine?

And all that is without even going into the inherent fuzziness behind any mathematical/computational system -- math has to be defined in terms of human language at some level, or defined implicitly. There're always gonna biases, undeclared/implicit axioms, or unclear definitions.

If a perfect, idealized system can only exist in our brain, which is itself incredibly fuzzy and imperfect, can it truly exist?