There are several ways of approaching that particular question. And none are simple, actually.
First, just to frame why 0/0 is so weird, consider 1/0. Asking “what’s 1/0” is like asking “what number when multiplied by 0 equals 1?” There’s no answer because any number multiplied by zero is zero and no number multiplied by zero is one.
So now on to 0/0. “What’s 0/0” is like asking “what number when multiplied by zero gives zero?” And the answer is “all of them.” 1 times 0 equals 0, so 1 is an answer. But also 2 times 0 is 0. And so is pi. And 8,675,309.
So, you could say that 0/0 doesn’t have a single answer, but rather an infinite number of answers. That’s one way to deal with 0/0.
Another way is with “limits”. They’re a concept usually first introduced in calculus. Speaking a bit vaguely (though it’s definitely worth learning about if you’re curious, and it seems you are), limits are about dealing with “holes” in equasions.
Consider the equasion y=x/x. With only one exception, x/x is always 1, right? (5/5=1, 1,000,000,000/1,000,000,000=1, 0.00001/0.00001=1, etc.) But of course 0/0 is a weird situation for the reasons above.
So limits were invented (by Isaac Newton and a guy named Leibniz) to ask the question “if we got x really close to zero but not exactly zero and kept getting closer and closer to zero, what number would we approach?” And the answer is 1. (The way we say that is “the limit as x approaches zero of x divided by x is one.”)
Sometimes there’s still weirdness, though. If we look at y=x/|x| (where “|x|” means “the absolute value of x” which basically means to remove any negative sign – so if x is -3, |x| is positive 3) when x is positive, x/|x| is positive 1. When x is negative, x/|x| is negative 1. When x is 0, x/|x| still simplifies to 0/0, so it’s still helpful to our original problem. But when we approach x=0 from the negative side, we get “the limit as x approaches 0 from the negative side of x/|x| is -1” and “the limit as x approaches 0 from the positive side is (positive) 1”. So what gives?
Well, the way mathematicians deal with that is just to acknowledge that math is complex and always keep in mind that limits can differ depending which direction you approach them from. They’ll generally consider for their particular application whether approaching from the left or right is more useful. (Or maybe it’s beneficial to keep track of how the equasion works out for both answers.)
I’m sure there are other ways of dealing with 0/0 that I’m not directly aware of and haven’t mentioned here.
So, to wrap up, there are some questions in mathematics (like “what’s 0/0?”) that don’t have a single simple answer. Mathematicians have come up with lots of clever ways to deal with a lot of these cases and which one helps you solve one particular problem may be different than which one helps you solve a different problem. And sometimes “there’s no right answer” is more helpful than using clever tricks. Sometimes the problem can also be restated or the solution worked out in a different way specifically to avoid running into a 0/0.
It’s definitely unfortunate that they don’t teach some of the weirdness of mathematics in school. But something I haven’t even mentioned yet is that all of what I’ve said above assumes a particular “formal system.” And the rules can be quite vastly different if you just tweak a rule here or there. There’s not technically a reason why you couldn’t work in a system which was just like Peano Arithmetic (conventional integer arithmetic) except that 0/0 was by definition (“axiomatically” – kindof “because I said so”) 1. (Or 42, or -10,000, or whatever.) That could have some weird implications for your formal system as a whole (and those implications might render that whole formal system in practice useless, maybe), or maybe not. Who knows! (Probably someone does, but I don’t.) (Edit: looks like howrar knows and it does indeed kindof fuck up the whole formal system. Good to know!)
One spot where mathematicians have just invented new axioms to deal with weirdness is for square roots of negative numbers. The square root of 1 is 1 (or -1), but there’s no number you can multiply by itself to get -1.
…right?
Well, mathematicians just invented something and called it “i” (which stands for “imagionary”) and said “this ‘i’ thing is a thing that exists in our formal system and it’s the answer to ‘what’s the square root of negative one’ just because we say so and let’s see if this lets us solve problems we couldn’t solve before.” And it totally did. The invention(/discovery?) of imagionary numbers was a huge step forwards in mathematics with applications in lots of practical fields. Physics comes to mind in particular.
Indeterminate forms come from limits. It’s not the question you asked, and I think this answer was a little off the mark because of it. For the sake of shared knowledge, I will explain anyways:
When looking at a limit, it’s important to note that you aren’t working with zero (or infinity, or any number you are studying the limit of), what you are working with are numbers approaching the limit. For example, for (x+1)/(x), the expression has no equivalent value at x=0, as 1/0 does not exist. We can see why if we use the limit as x approaches zero. The numerator will approach 1, and the denominator approaches 0. The numerator has little impact on the value of the expression, but the denominator… dominates the value, for the pun. And, while we can’t evaluate at 0, we can put really small numbers in there and see what happens- and what happens is the expression becomes incredibly large. I’m sure that if you don’t see where this is going, you can go to Desmos or some other graphing calculator and try it for yourself.
As far as the indeterminate form- 0/0 is always undefined, at least in most mathematics. However, if you were to look at equations :
y = x/x
y= x^2^/x
y= x/x^2^
you’ll see the curves behaving differently around x=0. The first makes 0/0 look like 1, the second makes 0/0 look like 0, and the last will make 0/0 look like infinity*. Once again, note, however: 0/0 does not exist, and there is discontinuity on all of these curves at x=0.
*Edit: or negative infinity, I forgot that this limit doesn’t exist. Even though the limit doesn’t exist, it is still a useful example.
It’s a calculus thing. We can only give the expression a value if we know the functions giving us a zero value that are being devided. For example if we were dividing the function (X) by the function (X^2) at zero our we would get infinity (Wikipedia has a pretty good page on indeterminate forms).
You could also think of it like multiplying both the numerator and denominator of a fraction by 0. This should preserve the fractions value, but multiplying by 0 essentially erases both values so we can no longer know what the fraction equals unless we know how both values came to be 0.
There’s several factors at play here. An athletic heart is not only more efficient down to the conductance of the cardiac tissue, but it also has a larger stroke volume. With those 120 bpm each beat could be pumping 40cc of blood while in the other heart each beat might only be able to pump 30cc. This is because an athletic heart is able to more fully contract to squeeze out all of the internal volume. Think of the conductance of the heart as a snowy hillside. The first time you take a sled down the hill the snow hasn’t been compacted to make a path. The more often you take your sled down that path, the more compacted it gets and the faster you and your sled will go down the hill the next time. Plus I haven’t even mentioned blood pressure decreasing in an athlete due angiogenesis and dilation of already present veins and arteries.
So to summarize, it’s not just bpm that need to be accounted for here. You also have to consider:
conductance lowering the cardiac impulse threshold
Energy use increases with bpm, change in pressure (systolic - diastolic) and the stroke volume (amount of blood pumped per beat).
Note that there is also an inverse relationship between stroke volume and bpm because the faster the heart beats, the less time for blood to return to the heart for the next beat.
That said, heart “strength” is more about reserve capacity (ie ability to ramp up when necessary) than energy efficiency. It’s like comparing a Ferrari to a Corolla: at 100 mph the former can still increase its power whereas the latter is getting near its limit.
So if the Ferrari has a “car attack” and suddenly loses 50% of its max speed then it can still keep up on the highway, the Corolla maybe not. That’s more important than which one is more energy efficient.
Well, the context matters greatly here. If dehydration is severe enough to lower blood pressure (a.k.a. hypovolemic shock) it can cause long term brain, liver, kidney, and heart damage. That is assuming you survived. It could also cause local ischemia ( loss of blood flow) requiring limb amputation.
If it is not bad enough to cause shock, the most probable long term sequelae would be kidney damage. Dehydration can precipitate ATN (acute tubular necrosis). In a kid this may appear to be transient. It would kill a certain percentage of your available nephrons. As a kid, you only need ~20% of your nephrons to assume full kidney function. This would mean that you would appear to recover but would likely go into kidney failure at an early age.
There are also psychological effects depending on severity and duration.
Many herbivores have a part of the digestive tract devoted to fermentation (or other microbe based processes) to break down cellulose. This involves a community of microorganisms that live in that part of the gut, and it is those microorganisms that break down the plant matter, producing nutrition for the animal via the products of their digestion, or by the animal breaking down the microorganisms themselves. Ruminants in particular like cows with their specialized multi-compartment stomach devote a lot of space to culturing this microbe colony, but rabbits and horses are hind gut fermenters so they have cecum for that. Rabbits also are coprophagic (eat poop), they digest some of their plant matter once, then eat the poop pellet and send it through again so it can be broken down even more.
But basically, with the microbes doing the work of digestion, it is more about what they can extract, and the herbivores just host them. We have a different community of microorganisms than them, and our digestive tract wouldn’t be able to support large numbers of those species.
Fair criticism, and in regards to minerals especially, I totally failed to mention the need for herbivores to have access to literal rocks and dirt rich in different minerals that aren’t readily available in plant. In captivity, this takes the form of mineral blocks of course.
Humans mostly absorb iron through the duodenum, which is a very short bit of intestine near the stomach.
Herbivores, on the other hand, have either massively complex systems of stomachs, chew their cud to make nutrients more absorbable, or letting food ferment before digesting. The latter also works for humans, if you like fermented veggies.
Of course, diet also matters. Humans don’t eat all that high iron foods, but grass is a cow’s main food source and it’s high in iron.
This is going to cover the factors that affect the ability of humans to absorb Iron which isnt quite addressing your question directly but I would rather not speculate about things that I have not researched as thoroughly. Iron bioavailability depends on several factors including what you eat along with the Iron. Citric acid and protein significantly increase the bioavailability of Iron. Plant foods rich in phytate (what plants use to store Phosphorus) bind to and render unavailable metals like Iron, Zinc, Calcium etc but these levels vary significantly between plant food sources. Other metals like Zinc can interfere with Iron bioavailability and vice versa. And normally the body’s ability to absorb Iron is regulated such that Iron is absorbed more efficiently if you are deficient and less efficiently if you have an excess. There are a few disorders that cause this Iron regulation to malfunction either resulting in deficiencies or the complete opposite of this, excessive Iron that starts depositing in organs but with a physiologically “normal” person that regulatory system acts to normalize the amount of Iron absorbed to an extent.
I would argue it is a feature and not a bug. Your body controls the uptake of iron with hormones. Those hormones work less effectively on the uptake of heme, but I would say that is the bug. Hemochromatosis (abundance of iron) can present the same symptoms as iron deficiency. Both issues are usually caused by genetic issues rather than dietary ones though.
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