Most insects (bumblebees included) don’t simply flap their wings up and down. Each stroke (and both the up and down strokes) can be angled and turned depending on what they are trying to accomplish. Additionally they flap very fast. This combination of speed and variety of wing strokes allow many insects to change direction rapidly.
How fast are their wings? Synchronous flight muscles beat at 5 to 200 hertz (Hz), in those with asynchronous flight muscles, wing beat frequency may exceed 1000 Hz.
Not exactly about bumblebees, but this was the subject of an article on the BBC just a few days ago, though I couldn’t immediately find the original source:
Apparently they make subtle changes to each wing stroke to adjust their flight.
Being small gives you the same inherent advantages that being large gives you disadvantages: strength scales as a square of “size” (e.g. height), while mass scales as the cube. You know how you physically can’t get titanically large because eventually your muscles physically can’t be strong enough to move you, your heart can’t be large enough or strong enough to pump your blood, etc.? Well, the smaller you get, the stronger your muscles get, in relative terms. I can guarantee you that the fact that bees are small is a significant portion of the reason they’re so nimble. Their inertia decreases more quickly with size than their muscular strength does, so they can be physically capable of much higher accelerations than larger organisms.
Charged particles that move through a magnetic field are deflected at right angles to the field (Lorentz force). Since your brain operates via moving charges, very strong magnetic fields can affect brain function. It can cause can cause neurological effects such as vertigo or seeing flashes, particularly when the patient moves his head.
MRI use static magnetic field. So, you start increasing the strength, and at some point it will start doing damage, starting with brain and heart, major organs with some sort electric field.
In a strong magnetic field, any atom that has any magnetic moment starts lining up. For the most part this is no big deal; indeed, it is what makes MRI scans possible. In very strong fields, any molecule that has any magnetic moment at all (i.e. nearly all of them) start both lining up and elongating as the field interacts with their magnetic moment. This radically changes how those molecules interact with others; in other words, basic chemistry is changed. Since we rely on chemical reactions to survive, we wouldn’t last very long.
At some point Diamagnetism will take effect, since water is diamagnetic and we are mostly made of water. I think this is what will kill the organism at higher Teslas (not sure how high).
even an MRI scan will have noticeable effects on the nervous system.
[here’s one example] (http://www.sciencedirect.com/science/article/pii/S0960982211009353): some people get vertigo during MRI scanning; and everyone gets at least some degree of nystagmus, tiny compensatory eye movements. the theory is that the magnetic field is affecting the endolymph in the vestibular system, producing a false sense of movement.
the effects also depend on the orientation of the field, and the way it’s introduced. [Transcranial Magnetic Stimulation] (http://en.wikipedia.org/wiki/Transcranialmagneticstimulation) (TMS) is a popular technique for disrupting brain activity, using a magnetic field produced by a device pressed up against the skull. the field strength of a TMS device is in the same neighborhood as MRI.
so, i would think that with much, much stronger field strengths than are used in TMS or MRI, the effects would become more and more severe until seriously bad things start to happen. I can’t guess what, exactly. Someone around here can probably produce an estimate of what will happen at each increase in order of magnitude…
I feel this wikipedia article describes what kind of magnetic fields can be generated.
1.25 T field from permanent neodymium magnet
45T strongest maintained magnetic field
2.8 kT Strongest ever produced (using explosives)
Sound engineer here. If loudness level is the same for both sounds, main thing you will recognize is the timbre. Closest sound will have much more highs than further one, because highs are more easily absorbed by air and humidity itself. Further sounds tend to have rolled off top end.
Also microdynamics are kept with closer sounds, let’s say you have two voices – closest one will have breath sounds, some pops and crackles, you can hear saliva being swallowed and other tiny things that usually slip unnoticed. Furthest voice won’t have any of that.
Another aspect is room reverberation – closer you get, bigger the ratio between reverb and direct sound. Voice far away will sound as loud as room reverb. If you come closer to source, direct signal will get louder and room will stay the same.
Sorry for bad english, its not my first language.
Edit: our mind is one powerful signal processor. We acquire our knowledge and how its sounds even before birth, so a lot of things for our mind are easy, because we are so used to them, that’s why its so hard to understand why we can distinct different sounds. But with good training we are capable even more.
Remembering back to high school physics, low frequency wavelengths will travel further than high frequency wavelengths. When we hear a “sound” it is a combination of many different wavelengths of vibrating air. A sound played quieter and closer to the listener should sound brighter (more high wavelengths retained) compared to the same sound reproduced at a higher amplitude further away.
The shape of the outside part of the ear, the pinna, also helps us differentiate between sounds in front of us and sounds behind us by a similar mechanism. Some audio and electronics companies (eg. Creative, Bose, Samsung and I’m sure many others) exploit this to simulate surround sound from a stereo speaker set up. Like our vision, we have two sensors that let our brain perceive stimulus in three dimensions
I’m a neuroscientist that studies hearing. The main difference would be the difference in intensity (loudness) between your two ears, the Interaural Intensity Difference.
- A sound off to your left but very close will be much, much louder in your left ear than your right ear
A sound off to your left but very far away will be equally loud in both ears.
Your brain has special circuitry in the brainstem that does this math automatically, comparing the differences in intensity and arrival time between the two ears.
The shape of the pinna have nothing to do with localizing distance. Pinna are for differentiating between something in front vs. behind you, and the elevation off of the horizontal plane.
Natural sounds are mainly complex waveforms comprised of fundamental frequencies and their respective harmonics, as well as any additional timbre and tone based additives (yummy). Compile this with the environment they are in and you get additional things that add to the wave known as time based effects. Our ears perceive sonic distances based on time based and dynamic based elements.
Time Based :
The sound reflects off of multiple surfaces getting delayed, confused, and in the end arriving at the ears at slightly different pitches or delayed resulting in various levels of mangle or not-so mangled. Ambiance (and lack of) plays a part when the environment adds reverberation and echos from faint to large amounts. Group all these factors together and in the end our brains can tell calculate which sounds arrived at which ear first, last, or if they arrived at the same time as well as their ambiance structure and place them in our perceived stereo field.
Dynamic Based :
Lower frequencies travel further than higher frequencies. Thats why a voice up close to you quietly sounds crisp, and a voice yelled from across a hall sounds slightly dull (depending on the reflective surfaces). Also, back to the original waveform, a complex wave form will embody whichever character it is being delivered from at its velocity. You can consider the ADSR for Dynamics ( Attack, Decay, Sustain, and Release ), as well as Volume, Velocity, Tone and Timbre.
All these things help us perceive distance, location, and quality of sound.
In addition to the mentioned volume differences between ears, an important factor is that sound waves bounce, causing what is known in the sound engineering world as “reverb”, a certain “muddy”, or unclear, quality of the sound. It happens because unless you are in a completely open or completely padded environment, you hear not only the original source of a sound, but also all its early reflections overlapping in quick succession.
When the source of a sound is nearby, the original wave is much louder than its reflections, because it has travelled (proportionally) much less distance before reaching your ears. Therefore, you hear the original sound clearly.
On the other hand, a distant sound will require about as much distance to reach you as its early reflections, so you will hear several copies of the sound at similar volumes in quick succession, causing the sound to become muddier. Since you are accustomed to muddy sounds coming from distant sources, you will interpret the sound as distant, even with your eyes closed.
Audio engineer here.
Distance is perceived by changes in the timbre of a sound. Boiled down, timbre is essentially the complex, high frequencies that distinguish sounds and make them unique.
Here’s an analogy:
It’s easily compared to looking at a piece of art. Say, if you’re looking at a painting that’s arms length away, you’ll be able to potentially look at each brush stroke or irregularity in the surface of the painting with immense detail. However, if you look at an enlarged version of that painting 50 yards away, you would still see it, but you would undoubtedly have a lot of trouble seeing those same intricate, subtle details as you did when it was at arms length.
Imagine a violin player playing a note quietly immediately in front of you. You would be able to pick up on very discrete, high frequency information that makes up the timbre of that sound. Perhaps you might be able to hear the crispness of the hairs gliding over the bow.
Now if you heard that same sound at the same volume from far away, you might not be able to hear that same level of detail.
Sound waves lose intensity as 1/r^2, similar to gravity. This is basically because your “energy” is traveling as the surface area of an expanding sphere away from a source. This is common in gravity, e&m, etc.
Lets assume that the sound is either directly to your right. A close and quiet sound, like a single headphone, will decay MUCH more significantly. The difference in L-R volume between your ears is greater.
In a far away sound, where most of the energy is already lost (presenting a lower volume to you), there is less loss in the 10 inches between your ears compared to the possible miles the sound has traveled before hand.
Basically, if two sounds have the same apparent volume in your right ear, nearer sounds will be fainter in your left ear and farther, more intense sounds will be more equal across your ears.
Basically its the equivalent of “tidal forces” for acoustics, to bring back the gravity analogy. In this case, its the “tidal volume-difference”.
Many of these answers give you a physics based answer but they do not answer how the brain differentiates sounds. In fact, many of these answers are at least partially wrong in their definitions of timbre, which has nothing to do with our ability to process proximity or loudness. Here’s what we know so far:
The brain can differentiate three components of a wave (first is the actual mathematical component, second is what we interpret it as):
The signal’s amplitude (perceived as loudness)
The signal’s frequency (perceived as pitch)
The signal’s complexity (perceived as timbre)
When sound enters the ears, it will always enter one ear more rapidly than the other due to proximity. Once the proper frequencies are stimulated at the cochlea, the signals are sent to the brain stem. In the brain stem, some signals are sent to what are called the olives of the brainstem. There are two kinds of olives important for hearing: the medial (closer to the middle of the brain) and lateral (towards the sides) olives.
To process the sounds, each of these olives are specialized for a purpose. The medial olives are specialized in determining the proximity of the sound, and the lateral olives are specialized to process the loudness of the sound. So in your case, your brain could process the quiet signal or the loud signal’s proximity and loudness by this manner. Note that there is some crossover in functionality in the brain as well, but this is generally what their specialty is considered to be.
Now there is something that is not well known, and that is how the brain can differentiate between sounds that include the same frequencies at different locations and amplitudes. For example, if you are at a party and there is music and talking, with many of the same component frequencies, how does your brain know how to attribute each of these components to the right people? We’re still working on that!
Acoustics student here. As with direction of sound, the brain simply applies what it measured in previous environments. The brain has an idea of what sounds should sound like and assumes that the difference between what’s expected and what’s measured is due to the environment.
For example, if you’re outside and you hear a gunshot, your brain hears it, relates it to all the things you’ve heard like it in the past, notices that it was missing high frequencies and trailed off gradually rather than all at once. It therefore sends you the message that it’s far away.
The brain doesn’t know why it sounds like this, but it knows that when things sound like this, they’re usually far away. As everyone else is saying, there are a whole bunch of different factors which the brain uses in different cases.
If you can reverse engineer the things that make it sound like that, then you can apply it to whatever you like and trick the brain into sending you the “far away” notice.
Sound encodes a lot of positional information. With a lens, for instance, you could pinpoint the location of sound sources just like you could for light sources.
Without a lens you have to rely on differences in t between when the signal arrived combined with differences in amplitude of those two signals.
If you draw the set of all points that would account for the difference in volume between the two received signals, and the set of all points that would account for the difference in time between the two received signals (left ear and right ear if that wasn’t already clear), and then look at their intersection, you end up with a more or less bounded set. This is a big step, and we actually do this calculation (see passive sonar), but it’s not really good enough to get the information we are capable of extracting.
We pay a lot of attention to echoes as well. sounds that are very close to our ears tend to not have much in the way of echoes. (relative to volume), whereas a sound that comes from far away has many echoes with similar volume as the original signal.
I think passive sonar and acoustics account for most of how we range sounds, but other aspects of the signal such as it’s spectrum, influence how far it can travel. The most obvious example of this is with lightning, and it shows in two ways. The closer the lightning strike is to you, the higher pitch its thunder will have, and the longer you listen to thunder the deeper it gets (because the echoes have travelled farther). Assuming you have some information about the sound you are supposed to be receiving, you could also use this method to range it.
It is true that the timbre of the sound would change over distance (due to low frequencies travelling farther) but I think the MAIN difference would be in the reverberation/delays we hear from sounds far away.
I work with live sound and do sound recording as a hobby, and the best way to make something sound “far away” in a mix is through reverb. When sending a signal through a reverb processor, you can adjust how “wet” or “dry” thie signal is. A 100% dry signal would be only the original source, while a 100% wet signal would be only the reverb, none of the original. The more “wet” the signal is, the farther away it is perceived to be, because you are hearing a higher ratio of reverb to original signal. If a sound is very far away, most of the sound you hear has bounced of other objects along the way. You hear very little of the “dry” sound. So your brain decides that a sound that is mostly reverberated is far away.
Think about listening to a person talking in a room. If they are standing right next to you, you hear the “dry” signal from their voice, and it drowns out most of the reverb you would hear. If they are at the other end of the room, a larger percentage of what you hear is reflected off the walls and ceiling rather than coming straight from their mouth.
It all has to do with how fast the sound waves hit each ear and how loud it is. Using this our ears can localize where the sound is coming from. If something is directly in front of you, it’s hitting both ears at basically the same time. If something is to your left, it hits your left ear first, the sound does go sort of through your head to your right ear, but most of it goes around your head. Your ear hears it even more when the sound gets around your head and also when the sound bounces back off of say a wall and back to your right ear.
At super low frequencies, we have very little ability to distinguish where noises are coming from.
About 20 years ago I wrote a science fair paper about how all that was needed to electronically reproduce surround sound was two speakers. All because of the way that our ears are shaped. The shape of the ear is so that we can tell weather sounds are in front or behind, and combined with stereo hearing from two ears, we are able to localize any sound in three dimensional space (perhaps with some head movement for verification.). NONE of the judges believed it was possible to determine the direction a train was traveling from directly underneath! I got third place. But looking back I realize I had zero sources for any if my claims…
Interbreeding fails when organisms are sufficiently different, the more closely related they are, the better chance they have. Typically the organisms have to be within 2 chromosomes of each other in terms of total chromosome count. Humans have 46 chromosomes, goats have 60. Also, if the animals are of different genera it is quite unlikely that they will interbreed successfully. Goats are most closely related to sheep, and sheep only have ~~56~~54 chromosomes, and are a different genus. Hybrids of these are stillborn usually.
The degree to which a potential offspring can grow in utero is quite different depending on how related the animals are. Some will be stillborn, others won’t be able to conceive at all (such as humans and goats). There is no real way to broadly generalize the level of potential development.
Edit: lost a word.
It’s actually variable depending on the species involved. There are basically two categories, prezygotic isolation mechanisms and postzygotic isolation mechanisms. Prezygotic means before what you’re talking about, the male and female gametes fusing together. Postzygotic means after that happens.
During this explanation, I will be defining “species” by the Biological Species Concept, which says that two individuals are of different species if they cannot produce viable offspring. Viable offspring means a healthy offspring that can reproduce itself. For example, according to this concept, domesticated dogs, dingoes and all wolves are currently a subspecies of Canus lupus, and are not separate species.
Prezygotic Isolation Mechanisms
- Geographical: This is the mechanism that contributes to allopatric speciation (when speciation occurs after two or more groups of a species have been geographically separated for such a long time that they become separate species according to the Biological Species Concept, which I will define below). It basically means that the organisms live in different places and cannot reproduce. Maybe it’s because those places are too far away, or maybe one lives in antarctica and one lives in the Sahara desert, and either would die in the other’s climate. They will never interact, much less reproduce.
Temporal: Species have different mating seasons or times of day (think of plants, or insects) that don’t overlap.
Behavior: If your species has evolved a highly specific mating ritual, you will likely not mate with an individual that has a different ritual. This also applies to unattractive physiological qualities in potential mates.
If our two species are not affected by these mechanisms, for one reason or another, at this point they may attempt mating.
- Mechanical Isolation: The sex organs are not compatible.
Gametic Isolation: The gametes interact (in humans, the sperm gets to the egg), but for some reason are unable to unite. Reasons include: the gametes do not attract one another, the gametes cannot physically fuse, or the male gamete is inviable inside of the female reproductive tract.
So let’s say that the gametes have fused and we now have a zygote.
Postzygotic Isolation Mechanisms
- Hybrid Inviability: The fertilized egg fails to develop past the early stages.
Hybrid Sterility: The hybrid cannot reproduce. This is often due to an unusual number of chromosomes that produce non viable gametes. Think of mules, ligers, etc.
Hybrid Breakdown: This hybrid is not sterile, but as generations continue to reproduce their offspring are increasingly inviable.
In your example, humans and goats, there are several mechanisms at play. Behavioral isolation, for example, prevents goats and humans from wanting to mate generally. The stopping point would probably be gametic isolation, for several reasons (I suspect that there would not even be gametic attraction). If not, it would certainly be Hybrid inviability. I’ve done some research based on your question, but fortunately no one is studying when exactly gametes of goats and humans become inviable . . . I don’t think it would even be legal in the US. We know however, that we are different species from goats, therefore one of these mechanisms interrupts along the way.
The average divergence time to complete hybrid inviability between mammal species is 2-4 million years with an upper bound of around 10 million years (Prager and Wilson, 1974; Fitzpatrick 2004). While hybrid sterility, especially hybrid male sterility arises much quicker, OP’s question seems to be concerned with the rates of evolution of inviability instead. Intriguingly, the average divergence time to complete hybrid inviability in non-mammal vertebrates (birds and amphibians specifically, though I would expect similar results in fish and reptiles) is closer to 20 million years with an upper bound of around 50 million years (Prager and Wilson, 1975; Fitzpatrick, 2004). Understanding the causes of these differences is an important question in the field of speciation even today, however we have accumulated some data on the subject.
First off, many responses so far have discussed the role of karyotypic evolution in the cause of hybrid inviability. In this I think many are mistaken. While it is certainly true that differences in the number of chromosomes can cause problems for hybrids, those problems are almost universally in the sterility category. This is because meiosis requires chromosome pairing and if there are not pairs present, meiosis will fail resulting in sterility. Examples of this include mules (Wodsedalek, 1916), and many others. While meiosis is indeed extremely sensitive to chromosome complement, development does not seem to be adversely affected. This is clear in the heterosis present in mules and others. It also makes biological sense as even though their locations may differ, a full double complement of genes should be present in all F1 hybrids (with the notable exception of sex-linked genes). Furthermore, I know of no study that has found a difference in autosome number to cause hybrid inviability (though of course there are many studies showing that sterility is strongly affected).
So it remains to be seen why is there such a difference in the rates of hybrid inviability between birds/amphibians and mammals.
In the mid 1970s A.C. Wilson and colleagues proposed that differences in the rate of the evolution of inviability may be due to a higher rate of regulatory evolution in mammals than other taxa (Wilson et. al. 1974). This is a pretty good hypothesis and seems to be supported by other research, however it really only pushes the question back one step: why is there a higher rate of regulatory evolution in mammals than other vertebrates?
One likely answer to this question is: mammals have something that other vertebrates lack – a placenta.
To understand why the presence of a placenta is likely to cause rapid regulatory evolution, we need to talk briefly about mammalian reproduction and how it differs from reproduction in other taxa. Mammal offspring are obligate parasites of their mothers: all of the nutrients they need for survival and development are drawn directly from the mothers tissue. This results in a really strong conflict between the mother and her offspring over nutrient allocation. Mothers of any taxa have an evolutionarily selected level of care (resources) that they prefer to give, while offspring would often prefer more resources (Trivers, 1974). In things that lay eggs, the offspring have no say in the amount of resources they get from their mothers – females allocate resources to the eggs before they are fertilized and then lay the egg shortly after fertilization. In mammals however, the offspring can have a say because of the placenta. In mammals the offspring can send signals to the mother effectively demanding more resources. This conflict is thought to have led to an arms race between mothers and offspring wherein offspring develop strategies to take more resources while mothers have developed counterstrategies to defend their finite resource pool (Zeh and Zeh, 2000; Crespi and Semeniuk 2004). Furthermore, mammalian pregnancies are highly dependent on down-regulating the mother’s immune system (Siiteri, 1982). If proper down-regulation does not occur, the mother will mount an immune response and reject the offspring (similar to rejection of an organ in a failed transplant). Both resource garnering strategies and counterstrategies and immune system deregulation are often in the form of regulatory evolution and likely explain why mammals have a higher rate of regulatory evolution than other taxa.
Now, parent-offspring conflict played out in the placenta is a solid hypothesis for increased rates of hybrid inviability in mammals, and I have given a number of a priori reasons to expect that it would play a major role, but I have not given any evidence yet. So here we go: Elliot and Crespi (2006) showed that the invasiveness of a placenta is highly correlated within mammals to the rate of hybrid inviability. (Invasiveness is best thought of as one of the offspring’s strategies for taking more resources). This is strong evidence that inviability is very closely tied to placenta function in mammals and easily explains why mammals may evolve complete hybrid inviability faster than other vertebrate taxa.
edit: spelling and a point of clarification
Sources (sorry most of these are behind a paywall):
Prager, E. M., and A. C. Wilson. 1975. Slow evolutionary loss of the potential for interspecific hybridization in birds: a manifestation of slow regulatory evolution. Proceedings of the National Academy of Sciences 72:200–204.
Wilson, A. C., L. R. Maxson, and V. M. Sarich. 1974. Two types of molecular evolution. Evidence from studies of interspecific hybridization. Proceedings of the National Academy of Sciences 71:2843–2847.
Related question, and somewhat anecdotal.
In my High School biology class I was taught that in most cases the sperm and ovum of different species will simply not fuse together.
The species in question had to be very closely related for the surface proteins on the sperms to be able to react with the surface proteins on the ovum. I was given the lock-key analogy for it. So, a pigs sperm cell will never be able to fuse with a human ova on its own, while if the neanderthals existed today, there would be a good chance that their sperm would fuse with a human ova.
Is what I learned in school, 20 years ago, correct? Or is it a simple generalization, or has been invalidated by our current understanding of reproduction?
Chromosome count, and the egg itself, and the sperm stop this.
Chromosome counts must match, we have 23 split chromosomes in our sperm, where as apes for example have 24. Fusion may occur, but nothing will come of it.
Then theres the sperm and the egg. The sperm will give out enzymes to break down the outer coating of the egg, (multiple sperm are needed to reach the concentration to do this). The sperm also have a specific protein on them, which the egg will recognize, and once recognized, will allow the sperm to ‘endocytose’, (be engulfed) by the sperm, and fertilization has occured.
These variables differ from species to species, allowing only (usually) one species to fertilize its own.
Wow. I just remembered reading that us humans share a lot of similarities with Dolphins.
And after a quick google search i`ve found that dolphins have 44 chromosomes and humans have 46.
That being said, would it be more likely to have a successful mating between a human and a dolphin than a human and monkey?
And if not, why?
I actually did a report on this years ago in eighth grade. In 2003 human cells were fused successfully with a rabbit egg, and after being grown for several days they terminated it to harvest the stem cells.
In Minnesota the Mayo Clinic managed to replace the blood of a pig with human blood also. I believe he lived out a full life.
The term that’s most commonly used is “Human Animal Chimeras.” It’s led to a lot of medical discoveries, however it blurs moral and ethical lines. Very similar to the soviet scientist who tried to create an army of ape people for Stalin.
There’s more information here. http://news.nationalgeographic.com/news/2005/01/0125050125chimeras.html
Edit: I totally forgot about that picture of the cat-dog that was circulating reddit a while back. It’s the perfect example of interspecies breeding. The hybrid made it to fetal stages, but because the DNA was such a mishmash of cells, it was extremely underdeveloped and was stillborn. It had characteristics of both the cat and the dog. It was really creepy actually. If anyone shows interest I’ll try and find the picture.
Hybridization is not always disadvantageous. In some plants/animals it is selected for.
However, if hybrids are less fit, this is called a post-mating barrier to hybridization. This can be due to things like genetic disorders (inviability/sterility/ or other non-reproductive disorders) or hybrids not looking sexy to either species.
If hybrids are unfit, the post-mating barriers can be “reinforced” with pre-mating barriers. This can be anything from changing mating seasons so they don’t overlap, having the wrong shaped genitals, or even preferentially ejecting sperm when it is from the wrong species.
If species diverge in allopatry, meaning not in contact with each other, then they have no reason to create these reproductive isolating mechanisms. This is how we can get ligers and tigons. However, if the species come back into contact before they are completely divergent, and if the hybrids are less fit, then these reproductive isolating mechanisms are evolved to keep the species apart.
Yes it is.
Just as a drawing of a cube is a projection of a three dimensional object onto 2D space, you can create three dimensional objects that represent a projection of a hypothetical four dimensional object into 3D space.
Of course, just as a flat drawing of a cube is not the same thing as an actual three dimensional cube, a three dimensional projection of a tesseract is not the same thing as an ‘actual’ tesseract.
Personally, I prefer to think in terms of “slices”.
Think of a cone. Put its base on the floor. If you slice the thing horizontally, you get circles with linearly increasing radii. If you slice it vertically, you get half hyperboles. If you slice it parallel to its edge, you get a succession of parabolas.
Actually, forget I said that. Let’s use a really simple example: a sphere with its center at the origin. When you slice it horizontally, you get circles. For a sphere,
rho^2 = x^2 + y^2 + z^2
where rho is the three-dimensional radius.
x^2 + y^2 = r^2 gives the radius in the x-y plane (which we slice parallel to)
so rho^2 = r^2 + z^2, meaning that the radius of the circle that you slice depends on the height that you slice at. The corresponding radii look like a circle.
For a hypersphere, 4-dimensional radius^2 = x^2 + y^2 + z^2 + a^2
a is the fourth spatial dimension. If you slice the hypersphere parallel to a = constant, you get spheres with
4-d radius ^2 = 3-d radius ^2 + a^2
So, put a bunch of spheres next to each other, but with their radii increasing/decreasing in the shape of a circle. That’s my portrayal of a hypersphere.
I find this method easier than imagining projections. Just like you can think of a cube as a bunch of squares stacked on top of each other in 3-space, a hypercube is a bunch of cubes stacked on top of each other in 4-space.
Edit: I haven’t figured out how to do rotations yet. I would appreciate help on how to portray 3-d rotations in two dimensions. (I’m guessing you need to use polar coordinates of some sort, but holy crap describing a square in polar terms is masochistic.) I haven’t thought this through yet.
Think of a cube drawn on a piece of paper as the ‘shadow’ cast by a 3 dimensional object into the 2nd dimensions. If you held up a see-through cube and shine a light from above, the shadow you would see would be the 2D projection of a 3D object.
Now, bump that up one dimension with a 4th dimensional object projection in the 3rd dimensions. It’s hard to wrap your head around, but the shadow of a 4D object into the third dimension is called a tesseract or hypercube: (http://www.daviddarling.info/images/tesseract.jpg).
The tesseract is the shadow/projection of a 4D object in 3D. The added fourth dimension, most perceive as time, and thus the 3D projection moves with time, such as in this youtube clip (https://www.youtube.com/watch?v=5xN4DxdiFrs
– 3D object in 2D is the ‘shadow’ of the 3D object
-the ‘shadow’ of a 4D object in 3D is called a tesseract or hypercube
-example of tesseract: https://www.youtube.com/watch?v=5xN4DxdiFrs
One thing you have to remember, is that we can’t portray a 3 dimensional figure on a two dimensional surface, in order for it to be seen or portrayed, the paper must be visible in the three dimensional plane. We must be outside the 2 dimensional plane to mark the paper (adding in depth) and outside it to view it or interact with it. We are not the outside the three dimensional plane, so it stands to reason that it could be impossible to properly portray a 4 dimensional object (many consider the tesseract to be flawed.)
Another thing you have to remember is that we do live with four dimensions, three space dimensions, and one time dimension. So the four measurements that correspond are Length, width, depth, and longevity, these four things have to be present in order for an object to be present to us. Longevity is most often displayed with numerous pictures, or an infinite mirror effect (showing it in multiple “times” per say).
There is a sudden point at which astronauts immediately feel weightless — it is the moment when their rocket engine shuts off and their vehicle begins to fall.
Remember, Folks in the ISS are just over 200 miles farther from Earth’s center than you are — that’s about 4% farther out, so they experience about 92% as much gravity as you do.
All those pictures you see of people floating around the ISS aren’t faked, it’s just that the ISS is falling. The trick of being in orbit is to zip sideways fast enough that you miss the Earth instead of hitting it.
It seems a lot of these answers aren’t addressing the first part of your question, which has the common misunderstanding that there is no gravity in orbit. The weightlessness experienced by astronauts is, as others noted, due to the free fall they are in once they enter orbit. So yes, there is a sudden point when they feel weightless when the rocket stops firing. The gravitational pull of the Earth however has not changed much–it is almost as strong in low earth orbit as it is on the ground. In other words, their weightlessness has nothing to do with the Earth’s gravitation pull getting smaller since that is a flawed assumption.
[This page] (http://history.nasa.gov/ap15fj/01launchtoearth_orbit.htm) shows a graph of g-force on Astronauts during a Apollo launch (go to almost the bottom of the page), which is interesting, as the g-force drops to zero in between each stage firing. The graph does start at 1 g, so I assume the zero-g is “really” zero g for those instants between stages.
As long as engines are firing, there is some g-force. When they stop firing between stages, there is no force and the ship is (temporarily) in free fall, though already going so fast that the -9.8 m/s2 does not have enough time to cut the speed much before the next stage fired. Though I could be wrong on this point, but you can still be “in free fall” while going up. If you could skydive out of a jet shooting high up very fast, you would be in free fall and “weightless” even though you are still flying upward for a few seconds, depending on the plane speed.
You can be in space without feeling weightless, and you can feel weightless without being in space.
Try this: grab a dense, small object, like a beanie baby or your wallet. Jump really high on a trampoline, and on your highest jump, about halfway up, let go of the object. Don’t throw it, just hold it in front of your face, and let it go.
Then, watch its movement relative to your hands. It will appear to float for a moment (until you land). That’s because it is in freefall just you are.
An orbit is nothing more than a falling object, just like you are on that trampoline, so anything orbit appears weightless from the perspective of itself.
Astronauts become weightless not because there’s no gravity, but because in orbit they’re technically in free fall. Gravity is still 80% up on the ISS IIRC.
So you’d feel gravity as long as your rocket was accelerating upwards, then the moment the engines cut out you’d become weightless.
I think you might have a misconception that the reason you become weightless is that you leave the earth gravitational field. This is not true and the difference in gravitational pull between the ground and the ISS is minimal. The major reason is that you are falling. It is the same when you are in free fall on earth. You feel weightless. So the point you fall weightless is when you start falling (or start orbitting).
The weightlessness on the ISS you’re talking about is not due to being so far out that Earth’s mass has a negligible gravitational pull. It’s because the ISS is “falling” (i.e. constantly accelerating (i.e. constantly changing direction)) in a circle.
However, if you were to ride a spaceship away from Earth in a straight line then, yes, you would feel a Earth’s gravitational pull diminish with respect to the distance between you and Earth squared. (Note, however, that such a ship is likely to be accelerating very, very quickly. About 3 Gs, give or take. This is a very large acceleration, so whether or not you would actually feel this difference during travel is questionable. However, an appropriate measuring device would, in fact, see Earth’s gravitational pull diminish as the ship traveled away from Earth.)
Astronauts will feel weightless as soon as they are in free fall. Anytime the engines are firing, there will be a certain G force they will be experiencing. Interestingly, if you simply jump into the air, you’re “weightless” for a split second, because you too are in free fall.
The reason that astronauts are weightless for days, weeks, or months on end in the Space Station is because it is in a perpetual free fall called an orbit! =)
Add-on question: Does the weightlessness or freefall feel like being on an airplane when it suddenly hits the low pressure pocket and everything freefalls down for a few seconds? In other words, is it really like falling (but without the air brushing past you)? If so, how can astronauts deal with it so easily? Every time I’ve experienced momentary freefall (on planes, Hollywood Studios Tower of Terror, or just jumping down from somewhere) it makes me queasy. I’d love to float around in space but I don’t want to fall non-stop.
ok, so since we all understand that astronauts are actually experiencing free fall and not weightlessness, is there any difference between that feeling and what they would experience if they were millions of miles from earth?
I was asking about the travel between not the actual approach. Perhaps the Moon was a poor example.
Pretend you are traveling a far distance in space and just need to accelerate once or twice and the ship travels straight (because there is no air resistance to slow you). Are you still ‘falling’ or are you now being pushed and the side of your rocket with the thrusters on it is now ‘down’ and would you be able to walk around? Would this be possible only as you were accelerating?
The feeling of “weightlessness” is just the experience of all of your component particles being moved equally. Ironically, gravity is the only force which is sort of capable of affecting all of your components equally (there is very slight compression always occurring), so you feel weightless when the only force acting on you is gravity.
Do you mean genetically or in terms of the number of individuals rearing and taking care of a given offspring?
Edit: Challenge accepted, I’ll try to answer both with one species.
Marmosets sometimes live in polyandrous groups where more than one male participates in rearing the offspring of a given female. Furthermore, multiple males may copulate with said female. Now, here’s where the genetic bit may come in. Tetragametic chimerism is a form of genetic mosaicism acquired in utero. Two eggs are released, two separate sperm fertilize each, and then the eggs fuse. If the two sperm originate from two different fathers, technically there are three parents. “This is particularly true for the marmoset. Recent research shows most marmosets are chimeras, sharing DNA with their fraternal twins. 95% of Marmoset fraternal twins trade blood through chorionic fusions, making them hematopoietic chimeras.”
Edit: formatting, plus I misspelled a word and it made me grumpy
Just off the top of my head I know there are prokaryotes that can absorb and express genetic material from another cell. Although this isn’t exactly like ‘having another parent’, one organism could feasibly have it’s own genetics from a variety of sources. This process is known as Transformation. I learned it from this experiment in Biology many years ago.
One way a seedless watermelon is produce is exposing a regular watermelon to a mutagen derived from the sap of the crocus flower. this results in plants with 4 sets of chromosomes vs the normal 2 sets. the tetraploids are then crossed with normal 2 set plants witch results in plants with 3 sets of chromosomes or tripoloid. the resulting Watermelon plants develop seedless fruit. Similarly seedless banana are also Triploid. commercial stew berries on the other hand have been mutated and crossed so many times that some plants have 10 pair of chromosomes
There was an article in science a few months ago about a new procedure called mitochondrial DNA replacement therapy. It involves taking a females egg, and replacing the mitochondrial DNA with some from a donor. The resulting offspring have DNA from the mother, the father, and the donor. It can be used to fight genetic diseases in the mitochondrial DNA, and can help to treat infertility. It is currently being tested in monkeys.
Sorry for those of you without subscriptions who can’t see the article.
Getting the proper number of chromosomes is a major barrier to having more than two genetic contributors.
There are polyploid animals (meaning they have more than two copies of each chromosome), but stable polyploidy is rare because it interferes with sexual reproduction. Monoploids are also often sterile (edit: I don’t know much about bees). Essentially, as a higher-order animal, if you don’t have the right number of chromosomes it is difficult to breed. The usual exceptions apply to some flatworms, etc.
In addition, for any animal with an egg-cell the egg depolarizes as soon as it detects fertilization by sperm, thereby preventing any other competing sperm from entering. This is an important feature, as multiple sperm would mean multiple male chromosomes and instable polyploidy, leading to death or sterility. Not a good outcome.
As for plants, they can get all kinds of crazy with their number of chromosomes. Theoretically this would mean that they could freely reproduce with multiple gametes… little sex-cell orgies, if you will. Plants are not my speciality, but as I recall from my botany class about eight years ago they do have other barriers to fertilization.
So, in answer to your question, and based on numbers of chromosomes only, animal gametes cannot be stably fertilized by more than one sperm, while plants could theoretically be gamete swingers.
*edit:clarified a bit
Though this may foot the bill it is quite arcane.
What it describes is an organism, S.pandora, that reproduces both sexually and asexually. In sexual reproduction the male attaches to a feeding stage and impregnates a budding female. The female then separates from the feeding stage and attaches herself to another host, where the larva in her develops.
Well, clones can have multiple parents at multiple levels. There’s the DNA doner, who has two parents, so that could count as one to three biological parents. Then you have the egg donor; she donates mitochondrial DNA. Then there’s the surrogate, and after the offspring is born, he or she could have one, two, or more adoptive parents.
Generally no. Although having one parent is not particularly rare (parthenogenesis in animals, self-fertilization in plants). In humans it is possible for an egg to be fertilized by multiple sperm (polyspermy), however this almost always leads to a non-viable fetus.
also, MA and PhD in biology.
A little late to the party but I just read an article for a biology class on zygotes having 3 sets of parental DNA due to a mitochondrial disease in the biological mother.
Since you can only obtain mitochondrial DNA (which is separate from the rest of your DNA) from the maternal side, if there’s a family history of mitochondrial illness then the mother has little chance of having a child with functional mitochondria.
Enter a donor with healthy mitochondria: their mitochondrial DNA is transplanted to the egg cell either before or following fertilization and viola! you technically have 3 parents.
Well, there are many animals that use “communal mating” where many males fertilize a females eggs (ex: salmon) but I do believe that in the majority of animals it would be impossible as it would cause issues in the number of chromosomes supplied. So even if multiple males fertilize, there is only one true father.
Yes, the Tralfamadorians have done much research into this.
In all seriousness there are many species in which multiple gametes unit in order to form a zygote. Also many organisms which go through alternations of generations could be said to have multiple parents. DIatoms and Apicomplexa are just a few who have such odd reproductive cycles.