/sci/ - Science & Math

You forgot to multiply by the width of the rectangles.

Biophysics -- because it's a rapidly expanding field that is getting a lot of attention recently, and also, bonus Physics awesomeness.

(full disclosure: physics major)

>>1934697
Bonus points for appropriate Dresden Codak comic.

If I can borrow a concept from Accelerando, what will probably happen is that life itself will be legally recognized as a basic human right, implying that life extension is also a basic human right. Put it another way, death is the greatest threat to human freedom.

Sure, it might take a few revolutions to get there. But it will.

(Or, magick singularity nanotech, which also solves this problem. Not that it's impossible.)

>>1854119

The magnetic and electric fields are unified -- you may already know this. But why are they unified? Relativity.

Think of the magnetic field as the relativistic correction on the electric field. Without it, relativity would lead different reference frames to see different things. So, we have this CrAzY cross-product magnetic field that causes a slight perpendicular-to-motion force on particles. This makes sense, relativistically, if you think about it.

As a by-product of the math you can use to find this field using the laws for the electric field and relativity, you find the magnetic field has a divergence of 0 everywhere -- no sinks, no sources. Everything just flows around in loops. This is where Maxwell's equations come from. Also, this explains why there are no magnetic monopoles -- otherwise, the divergence would be non-zero, and one of {electric field, relativity, magnetic field} just broke.

>>1821532

It's actually not a coincidence at all. Photons live in a special frame where the time axis and a space axis have collapsed into one -- it's a purely three-dimensional world. They can't move in space without moving an equal distance in time -- hence light always moves in one light-second per second. This is one of the many hints we have that time and space are not distinct in any way.

Of course, I'm talking about light in a vacuum here.

>>1736383

The Birthday Paradox.

It's really easy to explain from first principles (with a dash of basic probability), and it is mind-bogglingly freaky the first time you hear of it.

The probability of two people having the same birthday in a room of 23 people is 50%.

For advanced mathers, you can segway into the birthday attack.

>>1725737

If something is moving past you at near light speed, it will appear shorter along the direction of travel. This is *Lorentz Contraction*, and it's the exact same effect as time dilation, but applied to a spacial dimension.

if *you* were moving near light speed compared to, say, the Milky Way, it's the same as the Milky Way moving near light speed past a stationary you. In this case, you would appear the same to yourself, but the galaxy would flatten out along your direction of travel.

This is one of the many features of relativity that suggest time and space are not distinct -- they're all just dimensions. We call one "time" as a convenience to our primitive simian minds.

>>1629779

I'll exclude wormholes (etc.) from this discussion, as it's not true FTL. It's just pushing two bits of spacetime closer together, instead.

If we want FTL, we'll have to find something fundamentally wrong with relativity. Even the most basic bits of special relativity imply that faster than light travel would utterly destroy causality. The standard phrase goes like "relativity, causality, and FTL: choose any two".

(and yes, causality would be a horrible thing to lose. Do you like your free will? Even if you don't think you actually have your free will, breaking causality would shatter any illusion of free will as well. I'd take causality over FTL any day, even if it means we're trapped in our own huge, empty neighborhood of the universe. )

>>1629582
>>1629560

Actually, the bits of Maxwell's equations governing magnetic fields claim that the flux through any closed surface is zero. This would prohibit monopoles.

Though, yeah, if you throw Maxwell out (and derived, updated versions) there's nothing in Physics that says they can't exist. Not many of us are ready to do that yet, though. :D

>>1629720

interrupting this thread to say "best use of kim ross on 4chan". Usually it's just naked kim.

anyways... proceed.

>>1618982

so you know, that Folland book is a gigantic heaping pile of shit. Almost all of the questions are just rote calculation (not theory) and, seriously, who writes a multidimensional calc book with a total of only 5 pretty pictures.

seriously.

>>1624378
>>1624389

Yeah, waves make great use of complex numbers. I recall bra/ket notation for quantum uses complex numbers implicitly.

I doubt you'll find a use that literally uses the imaginary component of a complex number as an "imaginary unit". When you get right down to it, complex numbers are just 2-space with some fancy multiplication rules and neat properties. We say <span class="math">i^2 = -1[/spoiler], and use this notation, because it's a handy mnemonic for remembering how to multiply complex numbers. It's no more fundamental than that.

(in fact, saying <span class="math">z = 5 - 2i[/spoiler] obscures the fact that we really mean <span class="math">z = (5, -2)[/spoiler]; this can sometimes trick us into thinking about complex numbers the wrong way. be careful!)

>>1575444
>>1573605

Large ie crystals can be mitigated by using sugar (as mentioned), which is super hydroscopic, by using alchohol (which usually kills at the amounts we would need), and by freezing VERY quickly, usually by cooling the thing to within a hair of freezing, then dropping the temperature rapidly. All of these avenues can be researched.

Incidentally, it's no coincidence that good ice cream has lots of sugar and a hint of alcohol, and that liquid nitro ice cream tastes great: small ice crystals make good ice cream.

(I swear, Good Eats has taught me more chemistry than school, despite my kickass chem teacher.)

>>1570757
>>1570744

Indeed :D

Well, it's good to have independent verification; I don't trust my lisp skills yet.

>>1570548

for the record, /sci/, I'm brute forcing this just in case we didn't get it.

>>1570659

also: yes, it is. Even if it's currently beyond our means.

At least, for most of the string theories. The ones that are just like "Huh maybe the universe words this way" and don't predict anything aren't science.

>>1570686

I've never claimed to only believe what can be proven false. I'm claiming that it's only called "Science" if it can be proven false.

I'm claiming that unless it can be proven false, arguing about it never gets any farther than what sounds more right. Often, it never gets any farther than "I'm right and you're wrong".

All evidence-based arguments are falsifiable. Everything else is just superstition. I'm not saying I have no superstitions: I'm just saying their not Science.

>>1570536

no.

"magical thinking" == believing anything that is not falsifiable

it's not possible to prove that anything is true, in the sciences. It is, however, possible to prove stuff false. You could prove evolution false, for instance, by providing a species that jumps in complexity over a short time span, like say, a human generation.

It is impossible to show that creationism is false, becuase the ultimate answer is "God did it". There's NO way of proving God didn't do it. It's not science. It's magical thinking.

>>1564896

It's actually extremely important *not* to differentiate between spatial and temporal dimensions, because it just muddies true understanding.

Space and time have the same units; additionally, what we choose to call our "time vector" (the direction we travel in spacetime by sitting at the same space coordinates) is different depending on our velocity. It may (read: always) even have a spatial component. So making a difference between the two doesn't really help.

We often call time the "fourth dimension", and distinguish it as "temporal", but that's just because it's easier to wrap our monkey brains around. It's no different from any other dimension: it is simply a degree of freedom for the location of an event.

(tl;dr; 1984-style: Time is space! Energy is Momentum! The speed of light is 1! We have always been at war with newtonian dynamics!)

Saying "time slows down" is a bit misleading, though easier to grasp.

First, wrap your head around this: distance in time and distance in space are *the same*, we just give them different units because they appear different. Start measuring distances in light-seconds, or just seconds. This puts the speed of light at a beautiful, unitless 1.

Now, we have our X, Y, and Z axes sticking out from some point on our ship. We also have a T axis, now, because why not? It's just another distance. The trick is that these axes start to skew themselves and mix together as they go faster and faster.

Asymtotically, as they approach c travelling towards +X, the T and X axes start to rotate on to each other. The net effect is that time appears to pass more slowly on the moving ship, and the ship itself looks shorter in the X direction. It's not actually shorter: it's just that some of it's length is now along the time axes. Likewise, their clock's still running fine, it just has to move through more space for each second. Time and space have mixed.

Of course, people on the ship would say exactly the same thing about us.

This is the whole point of relativity: there is no absolute coordinate system, or set of axes. They'll all start to twist out of shape, depending on their relative velocity, and there is no absolute rest velocity, so...

The other fun thing is when v == c, the X and T axes will *merge*, which makes sense: it is now impossible to move without moving equally in time and space, that is, with a velocity of 1.

>>1537660

or, for that matter, Alastair Reynolds. Particularly the bit in the beginning of Redemption Ark about the Conjoiner/Demarchist war.

Revelation Space

because...

things are sweet for a while on Yellowstone, then the Plague comes and fucks shit up politically, socially, and economically. The Demarchists and Conjoiners have a war, then the jackass son of the homicidal transhumanist Sylveste goes and triggers the universe's life antibodies. Which fuck shit up more. Then we finally hide in the coldness of space, find the like three other species that survived in the entire galaxy, and manage to eventually take them out.

Then the Greenfly come and FUCK US UP HARDER. Long story short, what's left of humanity is huddled on a small asteroid that was ejected from the galaxy and is heading out along galactic north, millions of years hence. Then we try to convince our past selves to let us through to their brane, and ...

Basically, SHIT IS CRAZY, and GRIM, but TOTALLY AWESOME.

Also: FUCK DAN SYLVESTE

A pound is a unit of force and a unit of mass, in the imperial system. And yes, it is both, but as you insist, I'll consider both cases separately.

200 pounds is the same amount of force on Earth as it is on the moon. It may take more mass to exert 200 pounds of gravitational force, but pounds does not refer exclusively to gravitational force. For instance, we use pounds per square inch to measure pressure, which is (force / length^2).

200 pounds of mass is the same on the Earth as it is on the moon. Even you convinced yourself of this, so I need not argue this point.

To make things clearer, just take the word pounds out of the equation entirely. When, ever, will the sentence "200 A is always 200 A" not make sense? It's a goddamn tautology!

tl;dr - I know where you're coming from, OP, but you just made yourself look dumb in front of dumb people.

>>1173908

The fact that <span class="math">\pi[/spoiler] has anything to do with circles is a trick of physics, not really math. The differential equation <div class="math">f''(x) = -f(x)</div> shows up everywhere in physics in oscillators and circular motion. It turns out that <span class="math">\pi[/spoiler] is the *unique* half-wavelength of one of the simplest functions that solve that equation. So, it shows up everywhere, especially when you get to quantum.

When you think about it, we really should have defined <span class="math">\pi[/spoiler] to be the whole wavelength, that is, twice what it is now. It gives equations for circles a pleasing symmetry in calculus. <span class="math">\pi r[/spoiler] for the circumference, <span class="math">\frac{\pi}{2}r^2[/spoiler] for the area, and for spheres, <span class="math">2\pi r[/spoiler] for surface area and <span class="math">\frac{2\pi}{3}r^3[/spoiler] for spheres. It's much easier to see the derivatives at work with this, and the pure mathematical definition is nicer.