I agree with Dirk Pitt: it is not exactly a causal relationship -- the Ph.D is incidental. Universities are a primary source of funding for research. Doing said research earns you a Ph.D. It's very rare to get a research position anywhere without advanced education, and it's very hard to do research without funding.
If you are dedicated to innovation and research, Universities and Ph.Ds are the modern well-beaten (and well-funded) path, not the cause of the innovation.
Keep in mind that light "speed" is the one constant in all frames of reference. It is the maximum attainable velocity because it is the vector length imparted on all matter. By "accelerating" we're really only changing the direction of our four dimensional vector. Light makes a pretty good measuring stick, because its vector is limited to 3 dimensions instead of four. Thus we can "see" what the length of our vector is across all four dimensions.
I'm not sure what this means. What vector and vector's length are we talking about here? Light's vector is limited to 3 dimensions? What does that mean, since light does travel through time. From my perspective, a 4D vector would be (x,y,z,t), which can either denote a relative position or by extension, a relative traversal of spacetime, starting at (0,0,0,0).
Now consider that the second line is a line with X velocity imparted by a rocket. Normally this would lengthen the vector as well as increase its angle.
By increasing the velocity, I would think that the angle would decrease towards 0, since more X would be covered in the same amount of T. As the angle increases towards 90, an object is actually going slower.
However, our universe appears to have an upper boundary of light speed. Thus the vectors remain equal in length.
I'm not sure how the invariance of light forces the vector's length to remain constant.
Thanks for all your attempts, but I think, fundamentally, I'm just going to have to study more on these subjects when I have the time. I'm a bit too grounded in Newtonian mechanics to be moved by concepts without some understanding of the underlying experiments and their mathematics. Though the Lorentz transformations make sense to me if we assume the speed of light is invariant, I don't yet understand all its implications or how relativists work with the integrated concept of spacetime.
IIRC, the CUA keybindings were created with a focus on text editing. C-z,x,c,v were chosen because they are easy for your left hand to press, while your right hand can be either at the keyboard (chars or navigation keys) or on the mouse. They were intended to bind to among the most frequently used editing commands, namely "undo, cut, copy, paste" respectively. fyi: C-x is "cut" which is basically a macro for "copy and then delete".
Aside from habit, I suppose the question is, what really are the most frequently used commands? undo/copy/pasting or suspend/break/quote? Job management (z,c) is certainly important and I certainly make use of them, but, in general, I do not think they are used as frequently. Quoting is also used, but I don't think it is very common (some people don't even know about it).
Theoretically, they are orthogonal concerns, and we might be able to have a different set of keybindings for each mode: one set for editing the command line, and another set for manipulating an executing program. Of course this doesn't account for "quote", and also has several pitfalls.
Sadly, I don't really use Macs, but I envy some of their design, which you mention.
Coming from the Windows world, the unix terminals seem ancient and insane to me: console programs not recognizing key combinations because of the limitations of terminal emulators. Having to hit "escape" twice because keys are transmitted in-band using the "escape" code, etc.
I've been trying to get readline to behave like a Windows text box, to make editing the command line more efficient for me. Currently, I'm just binding alt-c,v and alt-b to invisibly mark an area and kill or yank the text so I have some semblance of the text editing I'm used to. Every so often I muse about creating a nice text-mode program which implements CUA command line text editing and job management.
Note that I'm stating that unix User Interfaces tend to be less modular and NOT unix OS design in general, which can be very modular and clean.
The problem is that highlight/middle-click muddles and hinders the modular combination of logically simple and orthogonal commands to form more complex commands. i.e. By performing two actions upon highlighting (select AND copy), we cannot build an operation which "selects" without "copying" using this technique. As the author of this article observes, this greatly limits what you can do between performing a "copy" and performing a "paste"; namely, you cannot select anything else.
In a more modular system, highlighting serves a single purpose: selection. Subsequently, another command may be given to perform some operation on that selection. In this way we can combine a few simple and logically orthogonal commands to build a more complex command.
In fact, this is my complaint with the UI of *nix programs in general (e.g. text editors). Rather than logically and modularly combining a few simple orthogonal operations, a multitude of distinct key sequences are used. e.g. with CUA (Windows) keybindings, you have the navigation keys (arrows, home, end, pgup, etc.). Adding ctrl to the left and right arrows moves by words. On top of these navigation keys, adding shift causes selection of the text you navigate. Each addition has a clear and logical role in modularly forming the compound command. Selecting a line is as simple as Home, Shift+Down. Copying to the Clipboard does not impede any subsequent editing; the Clipboard is a logically separate entity.
Of course, additional macros can certainly be created which bind to any mouse and key presses in order to improve user efficiency, but these should exist on top of a simple, logical, and modular UI for combining commands. Hence, you are welcome to X's highlight/middle-click, but it is very important that there also be a logically separate Clipboard with explicit copy and paste commands for modularly creating compound commands.
This is why CUA (Windows) keybindings and style of editing are infiltrating the unix UI; because they are more modular and simple.
Part of what I was trying to illustrate (in my albeit quite verbose response:) ) is that this equation is incorrect -- or, at the very least, it is not the Energy equation and it is not the Momentum equation, so where does it come from?
You cannot equate the KE "going to the left" with the KE "going to the right", perhaps partly because KE is a scalar quantity which has no direction. The Energy equation for the rocket involves the conversion of Fuel's Potential Chemical Energy into Kinetic Energy (all without direction).
Let me give an example. I think we both agree on the Law of Conservation of Momentum, which is:
Mr*Vr + Me*Ve = 0 Hence, Mr*Vr = -Me*Ve
Dividing your KE equation "Mr*Vr^2 = Me*Ve^2" by "Mr*Vr = -Me*Ve", after simplification (on each side, an M and a V cancel), we get:
Vr = -Ve
This implies that "Mr = Me", which I think is unlikely for most rockets. Most rockets are much more massive than their exhaust: i.e. "Mr > Me" and, therefore, in order for momentum to be conserved, the exhaust velocity must be much greater than the rocket velocity: i.e. "Ve > Vr".
Hence, since we both agree on the conservation of momentum, your "KE_left = KE_right" equation seems to be incorrect.
mv2 ~= (Mr * Vr ^ 2) ~= (Me * Ve ^ 2)
I'm still not sure what "m" and "v" are here, since "Mr != Me" and "Vr != Ve". What is "m" the mass of? What is "v" the velocity of?
<--- Action Reaction --->
KE is not directional, so Action-Reaction does not apply to Energy, it only applies to Momentum.
Squaring the velocities changes them from a vector (which may have a negative value) to a positive scalar value.
True. In the general definition of KE, "V^2" represents the vector dot product "V*V" which is equivalent to squaring the magnitude of the velocity vector.
In 4 dimensions all matter "travels" (although that's an incorrect term, it's really just a vector length) at light speed. Thus 'v = light speed'. We'll represent 'v' as the constant 'c'.
"Light speed" is a measurement of distance over time (299,792,458 m/s). i.e. every second, light travels a certain number of meters. So I'm wondering, when an object is at rest in our frame of reference, where are the meters that the object is traversing every second?
2. There's a good reason why we can't change our vector to a negative value for the dimension of time. Consider a two dimensional vector problem. Let's say we are on a space ship speeding along the X axis at 10 meters per second. Now let's say we turn our space ship sideways and start thrusting along the Y axis. How much thrust must be applied along the Y axis to negate and/or reverse my velocity along the X axis?
By definition, they are all orthogonal dimensions so movement along one does not affect the other, though I do not see how that illustrates why we can't go backwards in time if it is just another dimension.
I've read other similar explanations of Quantum Tunneling and quanta existing in multiple states simultaneously. Recently, I've read about quantum entanglement which illustrates a fascinating experiment that I'd love to play around with. Unfortunately, I still don't really understand them, and I have a great need to suspend belief until I can prove it to myself.
I'm not necessarily sure about the "mind-over-matter" stuff, but I certainly have no difficulty in considering that thought is non-deterministic in nature. What if we really *did* have multiple possible thoughts, but the one we actually think gets materialized by external or internal input? What if that's the core to intuition? I have X number of thoughts, and external stimuli forces thought Y into existence because it's based on the reality present arou
However, both E=mc2 and KE=(mv2)/2 define the energy for the rest mass (or current mass) of an object. It is very difficult to know what the rest mass of an object really is, because we don't know what fraction of c we are really traveling at any given time.
I'm not sure what "current mass" is, but I think they are different because "current" implies change (which seems more like "relativistic mass") and "rest mass" is a constant independent of the mass' velocity. "Rest mass" is always measured @ v=0 relative to our frame of reference, e.g. with a balance or scales (relative to other "rest mass").
I think each of your subsequent statements are true, but I don't quite see how they follow one another:
If we accelerate or slow down, we only have the reference stars and planets to define our motion.
Exactly; motion is defined as being between two frames of reference.
Light continues to exceed our own speed by 300,000 km per second, thus confounding our attempts to measure our speed.
True, we cannot measure our speed relative to light, since we are assuming (with evidence) that the speed of light is invariant wrt any measuring frame of reference.
Only a third party observer (e.g. a particle accelerator operator) would need to account for relativistic mass differences.
Right: only when (fr1) is traveling at near light speeds relative to some external frame of reference (fr2) does each fr have to take into the relativistic effects of the other.
(Mr * Vr^2)/2 = (Me * Ve^2)/2
Thus the total energy in the situation (minus any calculations for existing energy) is:
E = mv2
I don't think your first KE equation is valid (note that I added the "^2" which was missing from your post). Perhaps you are confusing the vector "Law of Conservation of Momentum" with the scalar "Law of Conservation of Total Energy"?
Note that it is the Conservation of Momentum (p=mv, sum of p = 0) that follows from Newton's Third Law that "every action has an equal and opposite reaction"; note the term "opposite" which indicates a vector (directional) quantity -- i.e. the velocity term has a scalar magnitude (the mass' speed) and a direction, which makes it a vector. By extension, momentum (p) is also a vector. This is important because adding vectors can be entirely different from adding scalars.
Variables which represent vectors are usually either in bold or have a line over them to indicate that they are vectors. Sometimes, I'm lax with that notation, but it is an important distinction here.
Application of the Law of Conservation of Momentum to the rocket problem would be:
MeVe + MrVr = 0
Note that Ve and Vr are technically 3D vectors, and therefore so is momentum. However, if we assume that all motion occurs along a single dimension, then we can represent the two directions of that dimension using positive (+) and negative (-) numbers and use simple arithmetic. However, in reality, the velocity vectors are 3 dimensional and complex interactions can arise, in which case more formal vector addition must be used (taking the vectors head to tail and drawing or calculating the resultant vector).
the total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system. In other words, energy can be converted from one form to another, but can not be created or destroyed.
Note that there are no vectors or "directions" involved with this law. There are several ways that "the system" can be defined. In the case of the rocket problem, I will define the rocket itself as being the "system", in which ca
Did they finally run out of characters for their operators? Is anyone else concerned that Perl is branching beyond the standard set of keyboard characters for their core language?
qw{... } gets a synonym:... . For those still living without the blessings of Unicode, that can also be written: <<... >>.
. ..
zip has an infix synonym, the Unicode operator ¦.
Unfortunately,/. will not display the unicode equivalent to <<... >>. Also note that '¦' is not a pipe '|', though the former is what the pipe key looks like on my keyboard.
Granted, these are still ASCII (>128) and currently just synonyms, but branching to unicode characters seems like a bad omen to me. Then again, IANA Perl programmer, so maybe I'm just blind to the joys of terse hieroglyphic code.
It's not a typographic error. Many people really have been taught that F=mv2 instead of F=ma or F=(mv2)/r. And that's my point. If you look around, you'll find all kinds of people using the incorrect formula of F=mv2.
Ah, I see. That's a shame. Is this really pervasive (in high school physics as you implied) or are some people simply accidently corrupting the equation for centripetal force? I'd think the fact that you can't do any calculations with it would make it obviously useless in physics class. From the sites, it looks to me like maybe some people just searched google and copied the text, without realizing that the formating might be messed up and they lose the R?;)
If we are to include relativistic considerations then, we must begin with the full equation:
E = (mc^2)*(1-(v/c)^2)^-1/2
You can't include relativistic considerations in E=mc2, because the speed of light is the only constant, regardless of your point of observation.
I'm not sure what you mean. You're right that the speed of light (c) is invariant, but relativistic mass is not (it is dependent upon velocity).
The postulate that light is invariant is used to derive the 4D Lorentz transformations between frames of reference, which appears as the factor gamma = "(1-(v/c)^2)^-1/2" in the equation above. So either the "m" in "E=mc^2" is "relativistic mass", in which case you must substitute "rest mass" times the Lorentz transformation, OR "m" is the "rest mass" and "E=mc^2" only pertains to the potential energy of matter at rest.
Take a look at Special relativity or the Kinetic Energy and Total Energy sections of Energy for the generalized "E=mc^2" equation and their examples.
I think this is accurate, which is perhaps part of why I don't understand your previous derivations for "Total Energy in a System = mv2" and "E=mc2"?
I understood the gist of your examples; you did a good job of explaining them despite the missing ascii art. Thanks for the links. I'll read up on time dilation. I'm still confounded by time stopping at c even though light goes at c and interacts with our frame of reference; i.e. there is a sequence (implying time) to the existence of light no matter how dilated time may be in its frame of reference. Perhaps light itself is just a special case? I guess more study is simply required of me.:)
That is sad if your high school physics taught that... IIRC, 0.5*mv^2 = kinetic energy, not force.
High school physics have long taught this little gem. It's too bad it's incorrect. Not to mention that many people don't know that it's incorrect. For example, a quick googling comes up with links like this one.
Aside from relativity considerations for KE, I'm not sure what you are referring to that is "incorrect". The link you mentioned seems blatantly in error by stating that "F=mV2" (by which I assume they mean F=mv^2), simply because the units do not match on both sides of the equation: "F" is kg*m/s^2 which is Newtons (force), while "mv^2" is kg*m^2/s^2 which is Joules (energy). I imagine it is a typographic error of some sort?
Note that in this equation, "m" is "rest mass" and that the equation reduces to "E=mc^2" for stationary objects (where v=0). The page I linked to illustrates the derivation for actual KE, concluding that the error factor of the simplified equation "KE=0.5*mv^2" is:
Hence, for v/c=0.1, the Newtonian formula for kinetic energy is in error by less than one percent. For v/c=0.5 the error is approximately 20 percent and at v/c=0.8 the error is more than 50 percent.
"Every action has an opposite and equal reaction", therefore
Total Energy in a System = mv2
"As an object approaches the speed of light, its mass grows to infinity", therefore E=mc2
I'm sorry, but I'm not quite following; maybe you're going to fast for me. e.g. I don't see how Newton's Third Law entails "Total Energy in a System = mv2". Similarly I don't see how you derive "E=mc^2". Could you please elaborate?
It's not directional, it's dimensional!
I'm not clear of the distinction you are making between "direction" and "dimension". From my perspective, a "direction" is a unit vector within the framework of many orthogonal dimensions. Dimensions are often defined by such unit vectors.
My original point was that (from my understanding) "relativistic mass" increases only in the dimension of its velocity, and not in orthogonal dimensions. e.g. if a mass is travelling at 0.9c in the +x direction, the relativistic mass increases only in the x dimension, requiring infinitely more energy to accelerate it in the +x direction towards c. However, in the y and z dimensions, the "relativistic mass" is equal to the "rest mass".
You see, Einstein explained that everything in the Universe has a "velocity" of light speed.
I once read something similar to this which basically argued that everything travels at the speed of light, and it explained slower objects as actually traveling at a high speed in other dimensions (of which we are unaware) such that the sum of these vectors has a magnitude of c. I suppose it's possible, but I didn't know that that was what Einstein was saying. Of course, I'm just a novice at this point.
Now if we apply this to dimensions, an object at complete rest in our universe is going infinitely fast through time. An object traveling at light speed is a perfect rest through the fourth dimension.
I haven't really studied time dilation in depth yet, but my current rough understanding is that there can be relative compression or expansion (dilation) of time between two frames of reference. Is time dilation spatially directional like relativistic mass?
In light of this, I don't quite understand your two statements:
1) an object at complete rest in our universe is going infinitely fast through time. "Completely at rest" and "infinitely fast th
It's certainly possible to get heavy metal poisoning from plutonium or uranium, but in practice the radiological consequences would kill you long before you saw any chemical effects.
With high enough doses, I can see that. But I was wondering if in smaller doses, which may seem to have little to no effect, there actually are non-fatal effects such as the more subtle symptoms I mentioned.
I'm still trying to evacuate some of high school "physics" that exists in my brain. (Did you know that force != mv2? Grr... Stupid high school physics.)
That is sad if your high school physics taught that... IIRC, 0.5*mv^2 = kinetic energy, not force. Or did you mean F=ma and you're referring to the insufficiencies of the Newtonian model?
I think that the Newtonian model is only significantly false at near light velocities (and therefore quite useful for many cases), at which point the relativistic mass changes wrt direction. i.e. it becomes more difficult to accelerate in the same direction as its current velocity, but not in orthogonal directions (relativistic mass is directional!).
A recent slashdot article (parallel dimensions?) renewed my interest in this and I've been reading about QM and the amazing entangled photons. As usual, slashdot wastes time I do not have, but it's so much fun.:)
The treatment (AFAIK) is for the cancer. There's a certain hormone that must be taken in order to replace the Thyroid's function.
Ah, I see. You were talking about continuing treatment of I-131 (or other I-radioisotopes) for thyroid cancer, not continuing treatment of stable I for the Chernobyl victims to protect their thyroid? Unless, of course, the Chernobyl victims continually ingest more I-radioisotopes.
It is kind of ironic that Iodine radioisotopes can cause thyroid cancer, and if the cancer exceeds some threshold, more Iodine radioisotopes are used to treat it by destroying the thyroid cancer.
Thanks for the good info. I enjoy reading your posts; they're certainly deserving of the "informative" mod.
I might suggest bolstering what I say here with some research on the Internet, but the Health effects of radioisotopes break down by the type of radiation they release.
In addition to the type of radiation, I imagine chemical reactions with the substances themselves must also be taken into account, as you indicate with the use of Sr-90 for Ca and I isotopes for stable I.
Alpha particles are basically free protons.
I thought an alpha particle was a helium nucleus (2p,2n)... though maybe you meant that it simply behaves somewhat similarly to a single proton? I don't thinks so, but I don't really know.
Oh, and anyone who doesn't get enough Iodine in their diet shouldn't eat an Iodine radioisotope. That tends to result in Thyroid cancer as in the case of many Chernobyl residents. Most of them were treated, but they still have to make sure they receive regular treatments or they will die.
As I understand it, the thyroid absorbs Iodine, so ingesting stable Iodine will take the place of the radioactive Iodine in the thyroid, and when the thyroid is at capacity, the excess Iodine can be excreted. It's interesting that continued treatment is required, perhaps to further dilute any remaining bad Iodine? It's also interesting since I thought Iodine isotopes had a relatively short lifetime?
Someone once told me that radioactive Iodine could be created by striking stable Iodine (within the human body) with x-ray radiation, but I thought a neutron was required to strike the nucleus for such a modification; unless the x-ray can trigger the release of a neutron from some other molecules in the body? Any thoughts?
Actually, the intent of my previous post was to question whether more subtle chronic problems could arise from smaller quantities of these heavy metals or radioisotopes, whether that be a lowered immunity, reduced nutrient absorption (Sr-90 in place of Ca?), or even general symptoms such as lethargy, depression, chronic pain, nerve damage, or other neurological deficiencies. In my imagination, I can see these substances or their radiation interrupting electrochemical processes beyond simply destroying DNA/RNA, but my actual knowledge of such experiments is quite limited. Though I suppose the subtle and complex nature of such symptoms may limit our ability to determine a causal relationship.
Thanks for the links. It's fairly clear from your Nader article that plutonium is not "the most toxic substance known to mankind." I can only assume that he was using hyperbole or some context, since it is obvious that there are more toxic (deadly) substances.
My concern is not only the mortal effects of heavy metals or radioactive substances, but also any chronic problems created by or exasperated by such substances. Obviously, this is dependent upon the specific substance and the particular patient (e.g. where the substance accumulates), but I imagine some general per-substance conclusions can be drawn from those people who have been exposed?
I'm glad we agree for the most part. Iraq might not turn out peachy, but despair leads to defeat at critical times such as these. Morale is key to any success. In a very real sense, more than any physical violence by terrorists (which will ultimately be futile in the face of the US's superior military), I believe the destiny of Iraq will be dictated by people's attitudes, both domestic in Iraq and abroad.
It is important not only to truthfully analyze and correct the bad actions of the US in Iraq, but also to weigh them in balance with their good actions, lest we attain a distorted view and lose the morale required to achieve our lofty goals. Sorry if I'm waxing rhapsodic.:)
I suspect that our major differences of opinion are in the means, not the end. I believe that violence begets violence, and in the long run, peaceful solutions are the only kind that lead to lasting peace.
I appreciate your perspective: peace is a noble goal. Violence often does beget violence, but that simple statement does not reflect the morality of either side, which is the salient question and a greater virtue than peace.
Making people scared leads to more war, not less.
Fear can lead to more war, but not necessarily. The act of scaring and who are scared is a broad and complex situation. Perhaps ideally, would-be criminals should be scared, while innocents should not be.
People with nothing to lose don't just roll over and give up at the first sign of a struggle.
Though they may not realize it, everyone has something to lose and something to gain. The key is to promote that realization. This is so tied to perception that it is an excellent illustration of why people's attitudes and by extension public relations and propaganda are so important.
Investing people into our system, so they have something to lose if it fails, is the only long term plan for ridding the world of violence, IMHO.
I agree; that is an excellent tactic which will be necessary for Iraq to succeed as a democracy. Unfortunately, that same tactic can be used for ill, and hence justice must still be the goal and not merely "ridding the world of violence".
e.g. Developed countries and their institutions such as the World Bank manipulates other countries, for good or ill, largely by non-violent economic means. Monetary and commodity dependence has crippled many nations. Corruption often becomes rampant, and internal violence is a common result.
Of course, it works both ways. The US is also borrowing obscene amounts of money. In a sense, much of the world is dependent upon the continued economic success of the US. There are ties that bind us all, if we are willing to see them.
Hence, IMHO, peace must be subservient to justice.
Get back to me when that safe and stable democracy you're hoping for materializes.
Implying what? That it is unlikely because it's so difficult? Just because it is difficult and will take a long while doesn't mean it is not worth fighting for.
First open election and the Shias win and throw the whole thing out. Or do you propose we keep our noses in the whole thing forever, to keep it 'fair'?
I suspect the US will play a key role in the future "security" of Iraq, partly to prevent significant reversion.
Iraq was never an immediate threat.
Based upon our current intelligence, you are correct; Iraq was not an immediate threat, but at the time prior to the war it was believed to be fairly immediate. Though, I'm not sure fascists would rejoice or be heartened by this fact, nor by how vicious the US can be.
The mistreatment of prisoners was encouraged from the highest levels and only stopped when it was made public.
I assume you are referring to Hersh's article? While (as far as I know) that is disavowed by the Pentagon and only substantiated by anonymous sources, I tend to believe it -- i.e. that there was a special operation which allowed a highly trained select group more autonomy, including intense interrogation, that grew wildly out of control. From my understanding, investigations were proceeding prior to public revelation about Abu Ghraib. Of course, it is aspects of this continuing story that is heartening those who would see the US defeated in its goal of an Iraqi democracy.
Most of the hijackers were Saudi Arabian, why did we not go after them? No link between Al Queda and Saddam has yet been proved. Why do we continue to support dictators across the world, like our friends the Saudis, who last time I checked were a monarchy who tortures people, suppressed dissent, and does all the bad things Saddam did?
IIRC, there are lose links between Al-Qaeda and Saddam, and definitely between Saddam and terrorism. Your questions seem good -- I'd like to know truthful answers to them as well. Maybe Saudi Arabia cooperated in all the right ways? Maybe Iraq was just an easy evil target who was bucking the US and UN? I dunno, but your good questions do not diminish Iraq as a target, but rather seem to include Saudi Arabia.
Trading Places was a good movie, but are you seriously using a fictional movie as evidence for your argument? Such power they have to warp our perceptions of reality. Of course, accurately predicting commodity futures is child's play, so you may have a point... or maybe you were referring to the ease with which anyone can use inside information?:)
If history is any indication, removing Saddam improves everyone's security in the long term. Perhaps you are too focused on the short term. The security of our troops is certainly worse now than before invading Iraq, though they are fighting in Iraq rather than in the US and terrorists are making themselves known by attacking.
The world is less one evil and rebellious despot, with the hope of replacement with a democracy in a region generally bereft of them. Current security must be weighed against future security.
What kind of myopic view leads you to characterize the US action as "imprisoning and torturing innocents"? Is the "torture" and other failures so prevalent that it somehow counters the good that the US is doing by working to instill a safe and stable democracy for the Iraqi people? (which is what I surmise the gp meant by the "right thing").
What standards has the US set that the fascists are rejoicing about? Is it that mistreatment of prisoners will not be allowed? Is it the replacement of a fellow fascist with a democracy? or is it that the US will attack anyone they believe is an immediate threat?
The Iraqi War encourages neither the US nor other countries to wage a similar war. I can only assume you are not rightly divining the current political situation in the US or the world if you believe that Iraq will serve as a model for the future. The apparently flawed or weak intelligence regarding Iraq has raised the bar for future wars, not lowered it. With the current reticence established due to Iraq, unless absolute proof of an imminent threat were revealed, I find it highly unlikely that a similar "pre-emptive" war would be initiated by the US.
"Pick a scenario"? How about none of the above? Your (1) dystopia and (2) utopia scenarios have really opened my eyes that Bush and America's dominance are the root of all evil./sarcasm. No offense intended, but to believe that failure in Iraq somehow equates with (2) reeks of some kind of propaganda. By that logic, just remove America, and the world would be so much better for it.
I agree with your stated values. Peace is the ideal, but it is the compromises you are willing to make to achieve peace that defines the value and morality of that ideal.
Thanks, that was a fascinating read. It's almost written as a story. Still, I'm strongly inclined to believe it, though I'm a bit dishearted that their primary sources are unnamed. It'll be interesting to see what comes of it now that it has been denied by the Pentagon (though I suspect that is necessary for covert operations, so it tells us little). Hopefully, some solid evidence will come forth if it is true.
As the article relays, it seems that a reasonable sap which provided for limited autonomy for a well-trained group expanded wildly out of control. From the article, it looks like the sap became ripe for abuse because untrained persons were performing the interrogation and they expanded to prisoners for minor crimes who were not really suspect to have useful information.
OT: Another interesting turn of events is the (apparently unwitting) use of serin gas as an explosive device by some insurgents. I'm sure/. and the news will be rife with posts exclaiming the presence of one single WMD, initially found not by the Coalition, but by the insurgents who apparently didn't even realize what they had found.
well, that's a chicken and egg kind of problem, but the point is that the FCC licensed away all that spectrum *for free* and hasn't bothered to coerce the industry to fulfill their end of the bargain...
You're right, though the FCC did mandate that by 2007 all TVs must come with digital tuners (FCC pushes digital TV adoption)... along with digital copy-protection. So after that point, all TVs will necessarily contribute to the 85% digital household market share required before digital is mandated and analog is released.
in theory, that's the citizen's spectrum that they're using.
Yeah, but, in theory, "The People" are represented by their the government.
Thanks for the heads-up. Perhaps it is obvious that I am a novice at Taphonomy (I didn't even know the word before), but I did google before I posted my previous comment and found several sites suggesting that fossilization occurs with low probability, though I found no actual numerical probabilities in my quick search. e.g. Taphonomy: Death Is A Sure Bet, Fossilization Is A Long Shot
While skimming other excerpts, I developed the sense that the probability of fossilization across species varies widely, and furthermore that events which may rapidly bury species greatly increases the probability of their fossilization.
After re-reading my isolated statement that you quote, it occurs to me that I may have failed to communicate my question very well... I didn't intend to question whether there are generally a lot of fossils everywhere (which there are), but rather the probability distribution of fossilization across species (frequent) and similarly across the Earth as it relates to species (ubiquitous), particularly as they apply to 'The Great Dying' (an extinction line), which may have been a time of great upheaval -- perhaps even making relatively permanent changes in the environment which would then support a different range of species?
In any case, as a newbie, I can always use more info. Thanks for the link.:)
Thanks for the excellent link. Do you know of any more that go into variations on that entangled photons experiment? e.g. can it be done without a coincidence counter? or what if the polarizer was moved before p hits it, but after s is detected?, etc.
The experiment they provide leaves me in a quandary, itching to modify parameters to understand the extent of the relationship between the entangled photons. Fortunately, their explanation was very clear, unlike many presentations which depend heavily upon mathematical details. I'm looking for similar explanations of actual experiments which can help me understand better.
In fact, it'd be really cool if I could put together such an experiment and play with it, but I don't think that is currently realistic.:)
I'd mod you up if I could... I'd like to hear the answer to your final question. My thinking is that "measurement" is any kind of interaction. And, in a sense, since everything interacts with everything else, there is no total isolation.
It's my initial hunch that some people are misinterpreting the probabilities in the wave function, but, I'm a quantum novice in need of some direct and clear experimental evidence to prove or disprove that.
Thank you for your excellent explanations. I love slashdot because of experts like you and your clarity of presentation.
I remember reading about this in the past in wonder and having many questions, though I cannot remember them in detail now. It makes sense to me that we describe an electron's position using probabilities because so much is unknown, but not that an electron actually exists in all those positions until detected (since we can't force an electron to exist somewhere by trying to detect it, can we?). Likewise it doesn't make sense to me that an electron actually goes through both slits, but rather that its interaction with both of the slits causes the interference patterns (perhaps partially through electromagnetic interaction?)... i.e. perhaps it still only goes through one slit, not both.
Of course, I'm apparently not fully grasping all evidence of the wave-like nature of matter, but instead still trying to hold onto wave-like responses of matter to forces (themselves being the sources of these forces), like that of adhesion in waves of water.
Thanks again for posting and for the suggested reading. Hopefully, with enough study, I'll understand it someday.:)
But at best wouldn't that require a sufficiently sized random sampling of the entire Earth? Is fossilization so frequent and ubiquitous and the extinction line so obvious around the Earth that this can be determined?
Granted, your scenario would make sense for a region if we assume homogeneity over time and that those fossils are representative of all species in the area at the time.
But, as you indicate, it is just an estimate based upon some evidence; a reasonable guess. I suppose I just wish there were some standard way to convey the level of certainty based upon the evidence in these cases.
Slashdot Mirror
I agree with Dirk Pitt: it is not exactly a causal relationship -- the Ph.D is incidental. Universities are a primary source of funding for research. Doing said research earns you a Ph.D. It's very rare to get a research position anywhere without advanced education, and it's very hard to do research without funding.
If you are dedicated to innovation and research, Universities and Ph.Ds are the modern well-beaten (and well-funded) path, not the cause of the innovation.
Thanks for all your attempts, but I think, fundamentally, I'm just going to have to study more on these subjects when I have the time. I'm a bit too grounded in Newtonian mechanics to be moved by concepts without some understanding of the underlying experiments and their mathematics. Though the Lorentz transformations make sense to me if we assume the speed of light is invariant, I don't yet understand all its implications or how relativists work with the integrated concept of spacetime.
Thanks for an interesting discussion.
IIRC, the CUA keybindings were created with a focus on text editing. C-z,x,c,v were chosen because they are easy for your left hand to press, while your right hand can be either at the keyboard (chars or navigation keys) or on the mouse. They were intended to bind to among the most frequently used editing commands, namely "undo, cut, copy, paste" respectively. fyi: C-x is "cut" which is basically a macro for "copy and then delete".
Aside from habit, I suppose the question is, what really are the most frequently used commands? undo/copy/pasting or suspend/break/quote? Job management (z,c) is certainly important and I certainly make use of them, but, in general, I do not think they are used as frequently. Quoting is also used, but I don't think it is very common (some people don't even know about it).
Theoretically, they are orthogonal concerns, and we might be able to have a different set of keybindings for each mode: one set for editing the command line, and another set for manipulating an executing program. Of course this doesn't account for "quote", and also has several pitfalls.
Sadly, I don't really use Macs, but I envy some of their design, which you mention.
Coming from the Windows world, the unix terminals seem ancient and insane to me: console programs not recognizing key combinations because of the limitations of terminal emulators. Having to hit "escape" twice because keys are transmitted in-band using the "escape" code, etc.
I've been trying to get readline to behave like a Windows text box, to make editing the command line more efficient for me. Currently, I'm just binding alt-c,v and alt-b to invisibly mark an area and kill or yank the text so I have some semblance of the text editing I'm used to. Every so often I muse about creating a nice text-mode program which implements CUA command line text editing and job management.
Note that I'm stating that unix User Interfaces tend to be less modular and NOT unix OS design in general, which can be very modular and clean.
The problem is that highlight/middle-click muddles and hinders the modular combination of logically simple and orthogonal commands to form more complex commands. i.e. By performing two actions upon highlighting (select AND copy), we cannot build an operation which "selects" without "copying" using this technique. As the author of this article observes, this greatly limits what you can do between performing a "copy" and performing a "paste"; namely, you cannot select anything else.
In a more modular system, highlighting serves a single purpose: selection. Subsequently, another command may be given to perform some operation on that selection. In this way we can combine a few simple and logically orthogonal commands to build a more complex command.
In fact, this is my complaint with the UI of *nix programs in general (e.g. text editors). Rather than logically and modularly combining a few simple orthogonal operations, a multitude of distinct key sequences are used. e.g. with CUA (Windows) keybindings, you have the navigation keys (arrows, home, end, pgup, etc.). Adding ctrl to the left and right arrows moves by words. On top of these navigation keys, adding shift causes selection of the text you navigate. Each addition has a clear and logical role in modularly forming the compound command. Selecting a line is as simple as Home, Shift+Down. Copying to the Clipboard does not impede any subsequent editing; the Clipboard is a logically separate entity.
Of course, additional macros can certainly be created which bind to any mouse and key presses in order to improve user efficiency, but these should exist on top of a simple, logical, and modular UI for combining commands. Hence, you are welcome to X's highlight/middle-click, but it is very important that there also be a logically separate Clipboard with explicit copy and paste commands for modularly creating compound commands.
This is why CUA (Windows) keybindings and style of editing are infiltrating the unix UI; because they are more modular and simple.
Part of what I was trying to illustrate (in my albeit quite verbose response :) ) is that this equation is incorrect -- or, at the very least, it is not the Energy equation and it is not the Momentum equation, so where does it come from?
You cannot equate the KE "going to the left" with the KE "going to the right", perhaps partly because KE is a scalar quantity which has no direction. The Energy equation for the rocket involves the conversion of Fuel's Potential Chemical Energy into Kinetic Energy (all without direction).
Let me give an example. I think we both agree on the Law of Conservation of Momentum, which is:
Mr*Vr + Me*Ve = 0
Hence, Mr*Vr = -Me*Ve
Dividing your KE equation "Mr*Vr^2 = Me*Ve^2" by "Mr*Vr = -Me*Ve", after simplification (on each side, an M and a V cancel), we get:
Vr = -Ve
This implies that "Mr = Me", which I think is unlikely for most rockets. Most rockets are much more massive than their exhaust: i.e. "Mr > Me" and, therefore, in order for momentum to be conserved, the exhaust velocity must be much greater than the rocket velocity: i.e. "Ve > Vr".
Hence, since we both agree on the conservation of momentum, your "KE_left = KE_right" equation seems to be incorrect.
I'm still not sure what "m" and "v" are here, since "Mr != Me" and "Vr != Ve". What is "m" the mass of? What is "v" the velocity of?
KE is not directional, so Action-Reaction does not apply to Energy, it only applies to Momentum.
True. In the general definition of KE, "V^2" represents the vector dot product "V*V" which is equivalent to squaring the magnitude of the velocity vector.
"Light speed" is a measurement of distance over time (299,792,458 m/s). i.e. every second, light travels a certain number of meters. So I'm wondering, when an object is at rest in our frame of reference, where are the meters that the object is traversing every second?
By definition, they are all orthogonal dimensions so movement along one does not affect the other, though I do not see how that illustrates why we can't go backwards in time if it is just another dimension.
I've read other similar explanations of Quantum Tunneling and quanta existing in multiple states simultaneously. Recently, I've read about quantum entanglement which illustrates a fascinating experiment that I'd love to play around with. Unfortunately, I still don't really understand them, and I have a great need to suspend belief until I can prove it to myself.
I'm not sure what "current mass" is, but I think they are different because "current" implies change (which seems more like "relativistic mass") and "rest mass" is a constant independent of the mass' velocity. "Rest mass" is always measured @ v=0 relative to our frame of reference, e.g. with a balance or scales (relative to other "rest mass").
I think each of your subsequent statements are true, but I don't quite see how they follow one another:
Exactly; motion is defined as being between two frames of reference.
True, we cannot measure our speed relative to light, since we are assuming (with evidence) that the speed of light is invariant wrt any measuring frame of reference.
Right: only when (fr1) is traveling at near light speeds relative to some external frame of reference (fr2) does each fr have to take into the relativistic effects of the other.
I don't think your first KE equation is valid (note that I added the "^2" which was missing from your post). Perhaps you are confusing the vector "Law of Conservation of Momentum" with the scalar "Law of Conservation of Total Energy"?
Note that it is the Conservation of Momentum (p=mv, sum of p = 0) that follows from Newton's Third Law that "every action has an equal and opposite reaction"; note the term "opposite" which indicates a vector (directional) quantity -- i.e. the velocity term has a scalar magnitude (the mass' speed) and a direction, which makes it a vector. By extension, momentum (p) is also a vector. This is important because adding vectors can be entirely different from adding scalars.
Variables which represent vectors are usually either in bold or have a line over them to indicate that they are vectors. Sometimes, I'm lax with that notation, but it is an important distinction here.
Application of the Law of Conservation of Momentum to the rocket problem would be:
MeVe + MrVr = 0
Note that Ve and Vr are technically 3D vectors, and therefore so is momentum. However, if we assume that all motion occurs along a single dimension, then we can represent the two directions of that dimension using positive (+) and negative (-) numbers and use simple arithmetic. However, in reality, the velocity vectors are 3 dimensional and complex interactions can arise, in which case more formal vector addition must be used (taking the vectors head to tail and drawing or calculating the resultant vector).
On the other hand, the Law of Conservation of Total Energy states that:
Note that there are no vectors or "directions" involved with this law. There are several ways that "the system" can be defined. In the case of the rocket problem, I will define the rocket itself as being the "system", in which ca
From Synopsis 3: Summary of Perl 6 Operators: Unfortunately,
Granted, these are still ASCII (>128) and currently just synonyms, but branching to unicode characters seems like a bad omen to me. Then again, IANA Perl programmer, so maybe I'm just blind to the joys of terse hieroglyphic code.
The postulate that light is invariant is used to derive the 4D Lorentz transformations between frames of reference, which appears as the factor gamma = "(1-(v/c)^2)^-1/2" in the equation above. So either the "m" in "E=mc^2" is "relativistic mass", in which case you must substitute "rest mass" times the Lorentz transformation, OR "m" is the "rest mass" and "E=mc^2" only pertains to the potential energy of matter at rest.
Take a look at Special relativity or the Kinetic Energy and Total Energy sections of Energy for the generalized "E=mc^2" equation and their examples.
I think this is accurate, which is perhaps part of why I don't understand your previous derivations for "Total Energy in a System = mv2" and "E=mc2"?
I understood the gist of your examples; you did a good job of explaining them despite the missing ascii art. Thanks for the links. I'll read up on time dilation. I'm still confounded by time stopping at c even though light goes at c and interacts with our frame of reference; i.e. there is a sequence (implying time) to the existence of light no matter how dilated time may be in its frame of reference. Perhaps light itself is just a special case? I guess more study is simply required of me.
Thanks again!
Aside from relativity considerations for KE, I'm not sure what you are referring to that is "incorrect". The link you mentioned seems blatantly in error by stating that "F=mV2" (by which I assume they mean F=mv^2), simply because the units do not match on both sides of the equation: "F" is kg*m/s^2 which is Newtons (force), while "mv^2" is kg*m^2/s^2 which is Joules (energy). I imagine it is a typographic error of some sort?
If we are to include relativistic considerations then, we must begin with the full equation:
Note that in this equation, "m" is "rest mass" and that the equation reduces to "E=mc^2" for stationary objects (where v=0). The page I linked to illustrates the derivation for actual KE, concluding that the error factor of the simplified equation "KE=0.5*mv^2" is:
Hence, for v/c=0.1, the Newtonian formula for kinetic energy is in error by less than one percent. For v/c=0.5 the error is approximately 20 percent and at v/c=0.8 the error is more than 50 percent.
I'm sorry, but I'm not quite following; maybe you're going to fast for me. e.g. I don't see how Newton's Third Law entails "Total Energy in a System = mv2". Similarly I don't see how you derive "E=mc^2". Could you please elaborate?
I'm not clear of the distinction you are making between "direction" and "dimension". From my perspective, a "direction" is a unit vector within the framework of many orthogonal dimensions. Dimensions are often defined by such unit vectors.
My original point was that (from my understanding) "relativistic mass" increases only in the dimension of its velocity, and not in orthogonal dimensions. e.g. if a mass is travelling at 0.9c in the +x direction, the relativistic mass increases only in the x dimension, requiring infinitely more energy to accelerate it in the +x direction towards c. However, in the y and z dimensions, the "relativistic mass" is equal to the "rest mass".
I once read something similar to this which basically argued that everything travels at the speed of light, and it explained slower objects as actually traveling at a high speed in other dimensions (of which we are unaware) such that the sum of these vectors has a magnitude of c. I suppose it's possible, but I didn't know that that was what Einstein was saying. Of course, I'm just a novice at this point.
I haven't really studied time dilation in depth yet, but my current rough understanding is that there can be relative compression or expansion (dilation) of time between two frames of reference. Is time dilation spatially directional like relativistic mass?
In light of this, I don't quite understand your two statements:
1) an object at complete rest in our universe is going infinitely fast through time. "Completely at rest" and "infinitely fast th
I think that the Newtonian model is only significantly false at near light velocities (and therefore quite useful for many cases), at which point the relativistic mass changes wrt direction. i.e. it becomes more difficult to accelerate in the same direction as its current velocity, but not in orthogonal directions (relativistic mass is directional!).
A recent slashdot article (parallel dimensions?) renewed my interest in this and I've been reading about QM and the amazing entangled photons. As usual, slashdot wastes time I do not have, but it's so much fun.
It is kind of ironic that Iodine radioisotopes can cause thyroid cancer, and if the cancer exceeds some threshold, more Iodine radioisotopes are used to treat it by destroying the thyroid cancer.
Someone once told me that radioactive Iodine could be created by striking stable Iodine (within the human body) with x-ray radiation, but I thought a neutron was required to strike the nucleus for such a modification; unless the x-ray can trigger the release of a neutron from some other molecules in the body? Any thoughts?
Actually, the intent of my previous post was to question whether more subtle chronic problems could arise from smaller quantities of these heavy metals or radioisotopes, whether that be a lowered immunity, reduced nutrient absorption (Sr-90 in place of Ca?), or even general symptoms such as lethargy, depression, chronic pain, nerve damage, or other neurological deficiencies. In my imagination, I can see these substances or their radiation interrupting electrochemical processes beyond simply destroying DNA/RNA, but my actual knowledge of such experiments is quite limited. Though I suppose the subtle and complex nature of such symptoms may limit our ability to determine a causal relationship.
Thanks again for your excellent posts.
Thanks for the links. It's fairly clear from your Nader article that plutonium is not "the most toxic substance known to mankind." I can only assume that he was using hyperbole or some context, since it is obvious that there are more toxic (deadly) substances.
My concern is not only the mortal effects of heavy metals or radioactive substances, but also any chronic problems created by or exasperated by such substances. Obviously, this is dependent upon the specific substance and the particular patient (e.g. where the substance accumulates), but I imagine some general per-substance conclusions can be drawn from those people who have been exposed?
It is important not only to truthfully analyze and correct the bad actions of the US in Iraq, but also to weigh them in balance with their good actions, lest we attain a distorted view and lose the morale required to achieve our lofty goals. Sorry if I'm waxing rhapsodic.
e.g. Developed countries and their institutions such as the World Bank manipulates other countries, for good or ill, largely by non-violent economic means. Monetary and commodity dependence has crippled many nations. Corruption often becomes rampant, and internal violence is a common result.
Of course, it works both ways. The US is also borrowing obscene amounts of money. In a sense, much of the world is dependent upon the continued economic success of the US. There are ties that bind us all, if we are willing to see them.
Hence, IMHO, peace must be subservient to justice.
Trading Places was a good movie, but are you seriously using a fictional movie as evidence for your argument? Such power they have to warp our perceptions of reality. Of course, accurately predicting commodity futures is child's play, so you may have a point... or maybe you were referring to the ease with which anyone can use inside information? :)
If history is any indication, removing Saddam improves everyone's security in the long term. Perhaps you are too focused on the short term. The security of our troops is certainly worse now than before invading Iraq, though they are fighting in Iraq rather than in the US and terrorists are making themselves known by attacking.
The world is less one evil and rebellious despot, with the hope of replacement with a democracy in a region generally bereft of them. Current security must be weighed against future security.
What kind of myopic view leads you to characterize the US action as "imprisoning and torturing innocents"? Is the "torture" and other failures so prevalent that it somehow counters the good that the US is doing by working to instill a safe and stable democracy for the Iraqi people? (which is what I surmise the gp meant by the "right thing").
What standards has the US set that the fascists are rejoicing about? Is it that mistreatment of prisoners will not be allowed? Is it the replacement of a fellow fascist with a democracy? or is it that the US will attack anyone they believe is an immediate threat?
The Iraqi War encourages neither the US nor other countries to wage a similar war. I can only assume you are not rightly divining the current political situation in the US or the world if you believe that Iraq will serve as a model for the future. The apparently flawed or weak intelligence regarding Iraq has raised the bar for future wars, not lowered it. With the current reticence established due to Iraq, unless absolute proof of an imminent threat were revealed, I find it highly unlikely that a similar "pre-emptive" war would be initiated by the US.
/sarcasm. No offense intended, but to believe that failure in Iraq somehow equates with (2) reeks of some kind of propaganda. By that logic, just remove America, and the world would be so much better for it.
"Pick a scenario"? How about none of the above? Your (1) dystopia and (2) utopia scenarios have really opened my eyes that Bush and America's dominance are the root of all evil.
I agree with your stated values. Peace is the ideal, but it is the compromises you are willing to make to achieve peace that defines the value and morality of that ideal.
Thanks, that was a fascinating read. It's almost written as a story. Still, I'm strongly inclined to believe it, though I'm a bit dishearted that their primary sources are unnamed. It'll be interesting to see what comes of it now that it has been denied by the Pentagon (though I suspect that is necessary for covert operations, so it tells us little). Hopefully, some solid evidence will come forth if it is true.
/. and the news will be rife with posts exclaiming the presence of one single WMD, initially found not by the Coalition, but by the insurgents who apparently didn't even realize what they had found.
As the article relays, it seems that a reasonable sap which provided for limited autonomy for a well-trained group expanded wildly out of control. From the article, it looks like the sap became ripe for abuse because untrained persons were performing the interrogation and they expanded to prisoners for minor crimes who were not really suspect to have useful information.
OT: Another interesting turn of events is the (apparently unwitting) use of serin gas as an explosive device by some insurgents. I'm sure
Thanks for the heads-up. Perhaps it is obvious that I am a novice at Taphonomy (I didn't even know the word before), but I did google before I posted my previous comment and found several sites suggesting that fossilization occurs with low probability, though I found no actual numerical probabilities in my quick search. e.g. Taphonomy: Death Is A Sure Bet, Fossilization Is A Long Shot
:)
While skimming other excerpts, I developed the sense that the probability of fossilization across species varies widely, and furthermore that events which may rapidly bury species greatly increases the probability of their fossilization.
After re-reading my isolated statement that you quote, it occurs to me that I may have failed to communicate my question very well... I didn't intend to question whether there are generally a lot of fossils everywhere (which there are), but rather the probability distribution of fossilization across species (frequent) and similarly across the Earth as it relates to species (ubiquitous), particularly as they apply to 'The Great Dying' (an extinction line), which may have been a time of great upheaval -- perhaps even making relatively permanent changes in the environment which would then support a different range of species?
In any case, as a newbie, I can always use more info. Thanks for the link.
Thanks for the excellent link. Do you know of any more that go into variations on that entangled photons experiment? e.g. can it be done without a coincidence counter? or what if the polarizer was moved before p hits it, but after s is detected?, etc.
:)
The experiment they provide leaves me in a quandary, itching to modify parameters to understand the extent of the relationship between the entangled photons. Fortunately, their explanation was very clear, unlike many presentations which depend heavily upon mathematical details. I'm looking for similar explanations of actual experiments which can help me understand better.
In fact, it'd be really cool if I could put together such an experiment and play with it, but I don't think that is currently realistic.
I'd mod you up if I could... I'd like to hear the answer to your final question. My thinking is that "measurement" is any kind of interaction. And, in a sense, since everything interacts with everything else, there is no total isolation.
It's my initial hunch that some people are misinterpreting the probabilities in the wave function, but, I'm a quantum novice in need of some direct and clear experimental evidence to prove or disprove that.
Thank you for your excellent explanations. I love slashdot because of experts like you and your clarity of presentation.
:)
I remember reading about this in the past in wonder and having many questions, though I cannot remember them in detail now. It makes sense to me that we describe an electron's position using probabilities because so much is unknown, but not that an electron actually exists in all those positions until detected (since we can't force an electron to exist somewhere by trying to detect it, can we?). Likewise it doesn't make sense to me that an electron actually goes through both slits, but rather that its interaction with both of the slits causes the interference patterns (perhaps partially through electromagnetic interaction?)... i.e. perhaps it still only goes through one slit, not both.
Of course, I'm apparently not fully grasping all evidence of the wave-like nature of matter, but instead still trying to hold onto wave-like responses of matter to forces (themselves being the sources of these forces), like that of adhesion in waves of water.
Thanks again for posting and for the suggested reading. Hopefully, with enough study, I'll understand it someday.
But at best wouldn't that require a sufficiently sized random sampling of the entire Earth?
Is fossilization so frequent and ubiquitous and the extinction line so obvious around the Earth that this can be determined?
Granted, your scenario would make sense for a region if we assume homogeneity over time and that those fossils are representative of all species in the area at the time.
But, as you indicate, it is just an estimate based upon some evidence; a reasonable guess. I suppose I just wish there were some standard way to convey the level of certainty based upon the evidence in these cases.
... the same as distilled water (pure H2O)?
I was wondering about that 0C too, thanks to the gp for clarifying.