You've never seen the cliff

Take a moment to think about every time that you've been pushed to the "breaking point." Just what is the breaking point? Shouldn't the breaking point be where you absolutely can't take anymore and you either die, pass out, or shut down? You would think so, because that's how I would define it. However, with the way our minds are constructed, our brains have ways to keep us from even getting close to that point unless it is absolutely necessary for survival.

I'm posting this in hopes that you could realize just how deep your capabilities extend past your anticipation. Yesterday at track practice, I was pushed to the point where I literally thought my body was going to shut down and stop functioning. This was after the second set. There was actually a third set that I didn't know about. When I became aware of the next set, my brain went through a whole series of "this is rediculus's and he must be crazy's." But there was something different about my mood that day. I thought I would do a little experiment with my body. At this point, since completing the workout seemed hopeless, I would keep going until my body would tell me to stop. The going got rough, but my body would not give up no matter how much pain I was suffering. I was suffering to the point of insanity... no lie. But I kept going because I wanted to see just how far away that wall is. I want to know where that metaphorical wall is; the breaking point. Wouldn't you know it, I never actually did hit the wall. I was suffering to the point of insanity and yet I did not reach the breaking point. I may have been pretty close, but I probably could have completed another set or possibly two before my body began to shut down.

Even though all of this exertion made me insane yesterday, pushing myself to the same level at a later date would not have the same psychological effect because it has happened before and trust that the amount of pain I was suffering was ok. Therefore, even though it is extremely difficult, you must realize the large buffer between your pain threshold and your actual breaking point. You would be able to cut off your whole arm and survive. Think about that one for a second.

In order to test my pain threshold, right after writing this post, I stabbed myself with a sewing pin by slowly increasing the pressure until I could get it to bleed. It was very difficult and took a few tries, but eventually I just took a deep breath and really shoved it into my finger. You have to trust yourself and just do what your brain tells you that you are not capable of. You will surprise yourself, and your willpower will only increase. The exponential theory in a nutshell... do what must be done immediately and the rest will follow.

Conjecture about the formation of black holes and neutron stars

I have no background in this field, have done no research, and have done no experiments with this. Therefore, I do not claim that I am right about this in any way. I brought it up in hopes that it would generate some conversation with the other bloggers. I know that math doesn't really conduct good conversation, so I'll throw in a toss-up here.

A black hole is a concentration of mass that is so great that not even light can escape it's event horizon [Wikipedia]. A neutron star is the remnant of a supernova that has a density of approximately the nucleus of an atom, which is along the lines of 5x10¹³g/mL [Wikipedia].

First, let's talk about neutron stars, because while they have amazingly high densities, they do have a measurable density. Neutron stars form after the supernova of a medium sized star, perhaps about 3 times the size of the sun in diameter. They then get crushed down into a 10 or 20 km neutron star, called such because they have the same density as the nucleus of an atom. But why? How come a neutron star only consists of atomic nuclei with no space inbetween atoms?

Well, first, we must bring up math. Yeah I know... get over yourself. The universal law of gravitation is the following equation:

F_g=G*M*m/d²

Where F_g is the force of gravity, G is the gravitational constant [6.67x10^-11], M and m are the masses of two objects, and d is the distance between those two objects.

It is a curious question to ask about what happens when distance is zero. Theoretically, the force of gravity would approach positive infinity, and math breaks... intuitively at least. "But when I touch things, they don't suck me into them with their awesome gravitational powers." Well, yes, that's because the distance never actually reaches zero [at least in your experience]. You have never touched anything in your life because of electrostatic forces that repel atoms and molecules from coming in contact with eachother. These forces exceed 10¹⁰⁰ newtons at the atomic level [Abtained by a rough calculation of Coulomb's law.] The only thing keeping atoms from collapsing and allowing gravity to fuse them together is the electrostatic forces.

Now, what I think happens during a supernova is that the forces of the explosion are so great that they overcome the electrostatic forces [occurs at around 10¹⁰⁶N] and allow the atoms to become close enough to touch. This touch perhaps interferes with the electrons in orbit and electrons from different atoms attract the protons of other atoms. Therefore, with the electrostatic forces "disabled," the force of gravity is then allowed to pull the atoms together. It will pull them closer and closer with forces increasing quadratically as the distance decreases. Eventually, the atoms stop coming closer when the nuclei make contact with eachother. This is my conjecture. I'm sure that there are many theories out about the topic, but that's where Dave and Ed come in. I don't really feel like reading about it. I just like throwing out ideas.

This basically outlines my thoughts about neutron stars, but what about black holes? Black holes are so dense that they have what is called an event horizon, or a sphere that requires an escape velocity beyond the speed of light in order to get away from the black hole's pull. How the black holes actually form is very similar to what they do in general [take stuff and never give it back]. Let's think about the example with the neutron star. The only thing keeping the star from getting any more dense is some force caused by the protons and neutrons with which the star is made. According to my philosophy, there is an event horizon, whereby if the atomic nuclei are crushed with a certain amount of force and contract to a particular distance, gravity is increased to a point where it can continue to contract the nuclei even further... and in fact, without bound. As the matter contracts closer and closer together, gravity continues to increase without bound. Therefore, distance decreases without bound and the whole star becomes a single point in the cosmos, or a black hole. A black hole has no density and no radius. It is just an infinitly small chunk of matter sitting in space. The black hole is the result of a chain reaction of two nuclei that converged close enough so that gravity could pull them infinitly close to eachother. As the point of mass grew larger and larger, the event horizon grew basically to a measureable radius. The mass of the black hole is inversely proportional to the square of the event horizon radius, which basically means that the event horizon grows immensely from the single two atomic nuclei that it was born from.

Any questions, comments, or refutations... all are welcome.

Attn! Ignore the post about rotational volume!

I bet you already did. But anyway, here's the reason why you should, assuming that you cared.



The last entry I posted about rotational volume was incorrect.

Mr. Cole wasn't lying when he said that if you make up a rule about integrals, it will be wrong. But anyway, here's why it was wrong. The mean value cuts through the top of an integral, and divides it so that the total area above the mean value equals the total area "missing" below the mean value. If you're not sure what I'm talking about, go to the graph in my previous entry and observe how some of the area from the integral goes above the mean value and some goes below. These areas should be equal if it is a mean value.

Which is fine and dandy, but now consider this. A square unit that is right on the x axis as it rotates will form a cylinder with a radius of x and a height of x. Let's say that we move the square two units from the x axis. Now it will form a cylinder with a hole. These volumes are not equal because the square that was further away from the axis travelled further and thus took up more volume.

Because of this simple fact, the rotational volume of the area above the mean value does not equal the corresponding rotational volume of the area below the mean value. Therefore, the mean value cylinder incorrectly represents the rotational volume of the 2 dimensional object.

So in order to correctly find the rotational volume, this is what you would do.

You would find the sum of an infinite amount of cylinder volumes, much as you would find the sum of the area of an infinite amount of rectangles. Since an integral can be broken up into a bunch of little rectangles, each of those rectangles can form little cylinders that we can find the area of. So let's take the Riemann Sum formula and modify it.

Σ(f((k(B-A)/n)),k,1,n) as n→∞

In order to modify it, we will use V=πr²h to change each rectangle into a cylinder. In this equation, r is represented by the height of each rectangle, or f((k(B-A)/n)). Height is Δx because the height is ever decreasing.

So, plugging into the equation, we get:

Σ(πΔx*(f((k(B-A)/n)))²,k,1,n) as n→∞

Which can be rewritten as:

π*Σ((f((k(B-A)/n)))²,k,1,n)Δx as n→∞

Notice how the function inside the sum is squared. If we think in terms of rectangles for a minute, squaring the function basically means that we're squaring the height of the rectangles, which basically means that we're squaring all of the function values. Therefore, what we're really finding is the integral of the squared function.

Thus, the equation in terms of integrals can be written as such:

V = π*∫(f(x))² dx [a,b]

There you go, and sorry for the inconvenience. I know that you all flipped out when you saw my fallacious entry.

Lifetime++: A World and a Life Away

[Cross-Posted on Fourth Turning of the Wheel]

In 18 years, where will I be? My first reaction to that question is, "How the hell should I know?" If you'd asked me a year ago where I'd be in a year, I would haven't guessed anything close to my present state, and that's with me being required to stay in the same place because of restrictions.

However, that out of the way, let me give a possible solution. In 18 years, I'll be 36 and a half years old. At that point, I'll have been out of academia, at least as a student, for at least 10 years. That leaves me ten years to be just about anywhere in the world. Not to mention the 8 years spent in academia that would mold and shape my future.

Now, if I had a choice, I'll be doing something fulfilling. Well, that's a little vague. Hopefully I'll be doing research in nanobiotechnology that will get us / have gotten us out of the fuel quagmire we're currently in. I'll be continuing in my studies, because at that point I'll have to just to keep up.

The career is done. What else is there? Relationships? I don't know. I suppose that (hopefully) by that point I'll have developed my social skills to the point that I can easily deal in extroversion and introversion. I suppose if I'm going to get married I'll have done so by then. In fact, if I'm going to have kids, I'll have done so by then. Wow, in 18 years I'll be married and have kids. How the hell does that happen?

As I write this, I'm realizing how incredibly superficial all my answers are. I don't really feel like anything I'm saying I'll get done will actually add to the world. Maybe if I'd said, "Solve world hunger," or something like that. It just seems like all of the things I'm hoping to accomplish could already be easily accomplished right now. Interesting.

Maybe you guys will do better with this. Or maybe I'm just too stuck up in "the now" to think that far ahead.

Namaste.

In terms of other interests, I hope I'll still be health

Lifetime++: A Game

Here's an interesting thought experiment. Most of us have lived 18 years by now. Some of us just reached this milestone recently. Some are still a few years or months short. Regardless, we all have had something like that span of time pass between our birth and now.

What's in 18 years? Obviously we've changed a lot since our birth, more than we could hope to explain in a single blog entry How much will we change in the next 18 years? At that point, most of us will be 35 or 36. We'll be long out of 20s, long out of our "young adult" period. Where will we be? What will we be doing? Who will we be?

The simple question that opens up a whole can of worms: where will you be in 18 years?

My Final Thoughts on Peak Oil

Well, they're actually someone elses, but that's beside the point. Check out this really great post by Dave Pollard on peak oil. He basically distills any information he's got down to a very short post on what he thinks will, and won't, happen with peak oil. A great read.

Well, I'm done with Peak Oil for now. Look for a new post topic sometime today, definitely before 8 PM.

While I'm at it....

C'mon guys... you don't have to pay attention to my posts about math. You can post about your own topics. I'd be glad to give input on your topics of interest. While you decide what you're going to post about, I'm going to go into the current calculus work.

Rotational Volume. I'm not sure what you use it for, but I know that it has applications somewhere, mainly with torque and other spinny things.

Rotational volume is the volume that some 2 dimensional object covers as it rotates completely around an axis.

Any rotational volume can be represented as a Mean Value Cylinder if the 2 dimensional object is rotating around the x axis. A mean value cylinder has the same volume as the rotational volume, but it's volume can be calculated by using geometry. The radius of the mean value cylinder is the average value of the function over the given interval and the height of the cylinder is the length of the interval.

An illustration should help you out.

Here, we see some function integrated, then the mean value is found and a rectangle is created. The shape that a rectangle forms when rotated about an axis is a cylinder, which appears on the right. The rotational area can then be calculated by squaring the mean value and multiplying it by B-A and by π. This is because the volume of a cylinder is V= πr²h

The mean value is represented as the following equation:

1/(B-A) * ∫f(x) dx

The height is B-A

Therefore, the formula for rotational volume is:

V = π*(1/(B-A) * ∫f(x) dx)²*(B-A)

or

V = π/(B-A) * (∫f(x) dx)²

As for areas that are inclosed by two integrals, its basically the same thing, except that one of the cylinders is positive and one is negative. You add their volumes together and the result represents the rotational volume of some area between two curves.

Overachiever's Edition of Integration by Parts

For those who bored with current studies in calculus, I will provide some notes for the general purpose of anyone. I don't actually know how to integrate by parts, but I'm going to look into the textbook right now just for you guys. And for as Kenny's comment in calculus, "Why do you learn the new stuff if you know that we're just going to go over it in class and be bored?" Well, even though I'm bored as shit, there are still things that I pick up from the second lesson that I wouldn't get the first time. If I'm learning something for the first time in a classroom, I never completely get it. Whereas, if I walk into the classroom knowing something about the topic, I'm just sharpening my skills.

As Mr. Cole has stated, there is somewhat of a product rule for integrals, but its method is not mechanical in any sense. The method is called integration by parts, which is an expansion of the derivative product rule discovered by Leibniz. I've removed the x from the functions because it makes it way easier to read.

d/dx [ f*g ] = f*g' + g*f'

If we take the integral of this equation, we get:


f*g = ∫f*g' dx + ∫f'*g dx


If we let u= f(x) and v=g(x), which assumes du=f'(x) and dv=g'(x), we get:


uv= ∫u dv + ∫v du


However, the standard notation has it written as:


∫u dv = uv - ∫v du


I'm sure that this formula doesn't mean a heck of a lot to anyone, but here's how you use it. Let's use an example integration.

∫x*sinx dx

First, create a u and v substitution. Notice the integral ∫u dv. This is the formula that your integral should resemble, so you must find a way to substitute ∫x*sinx dx in a way such that it equals ∫u dv.

Well, u appears in the integral as plain old u, so assign one of the factors the u. The v, however, has been differentiated. Therefore, in order to correctly substitute into v, you must set the second factor equal to the derivative of v.

The corresponding step taken in the example is as follows:

let u=x
let dv=sinx

Therefore:

∫u dv = ∫x*sinx dx


So now all that's left to do is plug into the rest of the values:

∫u dv = uv - ∫v du

[to get the value of v, integrate dv]
[∫sinx dx= -cosx ]

∫x*sinx dx = -xcosx - ∫(-cosx) dx

Now evaluate the integral:

∫x*sinx dx = -xcosx + sinx + C


And voilà, there you have the Integral. That was easy, right?
Well the fun part is realizing that this only works for a select group of functions where the new integral formed is a product that can be determined by other methods. Have a great weekend guys.

Peak Oil -- Peak Ignorance

I see it thusly -- We need to focus on long-term solutions, but we also need a short-term fix, and we need it very quickly.

What we don't realize is how bad it really is -- fuel prices in Europe are outrageous, but thanks to things like Oil-or-Your-Lives programs, we're perpetuating the illusion of cheap petroleum-based fuel. That bubble needs to be burst before people will ever realize how low on oil the we really are. We've already sucked out all the easy to get to stuff -- now we're pumping water and such into wells in order to get to the hard-to-reach oil thats still left. Thats a bad sign!

What I see as a path to the future is this: A massive tax on petroleum-based fuels, something along the lines of $.50 /gal for gasoline. Tax money that goes no where else but one place -- governemt funding for both long-term energy solutions and short-term fixes. People would wake up and notice then.

Things like Ethanol are a good start -- but there needs to be a greater incentive for people to buy cars that use it (and for stations to carry it -- if its everywhere, people will be more likely to use it). Heck, even place a tax on low-performance cars (your Hummers, etc.) that goes right back into a gov't subsidy on alternate-fuel cars.

Not that any of that will happen, seeing as the institution that needs to take that action (Gov't) is the same thing thats perpetrating the illusion.

But cars isn't just it -- nope. We need to move away from any petroleum product in our energy system too. Oil plans, nat gas plants, even old coal plants need to go. Clean Coal is one short-term solution, but I see fusion as being the Energy of the Future. Nuclear is too hazardous to warrant the construction of many more plants now (not that any new ones have been built in the last 30 years or so) but its a heckuva step up from oil.

But peak oil doesn't end on those 2 facets -- think about all the petroleum products used every day. Recycling is one option, but it isnt viable for all products. Reusing is a big step -- one that needs to be better implemented. But the biggest step that needs to be done is Reducing. Everything comes in a cardboard (recyclable) box, and then individually wrapped in little baggies of petroleum-based polymer. How are we going to eat our sanitzed food when theres nothing to wrap it in, eh?

And I'm done for now.

Hmm

Woooosh. I definitely didn't think about the post right before.

I wish I knew more about how they plan on replacing oil, because as far as I know, they don't currently have a replacement ready. That project with harnessing the sun's light directly sounds like it would work, but I personally think we have a bigger problem.

The problem is that as long as everyone is happy and has their energy, they're going to make babies, which means that (growth rate)^x is still in effect. Right now, that growth rate is still large enough to replace those that have died and then some. I have confidence that at some point, the growth rate will lower, but if it doesn't, the population will continue to rise. What I'm basically saying is that the end behavior of an exponential growth is +∞, meaning that energy demand will approach +∞, which means that unless we can supply an infinite amount of energy (I'm not saying that it isn't possible... who knows with quantum physics) we will always have to deal with deficits. Therefore, I think that the project where we use the sun's energy directly is only a delay in the inevitable (just like the class of '06). Not that it's going to matter much, because I'll be dead by then, but we all know how you feel about that excuse, lol.

Just making sure

Just making sure that I'm part of the blog because for some reason, the site wouldn't tell me that I was one of the contributors. Well... I'll leave it to DaveD to pick a topic because I can't think of anything that many people could respond to.

Peek-A-Boo With Peak Oil

[Cross-posted on Fourth Turning of the Wheel]

The worlds as we know it is about to change. In a very big way. And noone seems to care, or even know, for that matter.

Okay, so maybe that's a tad bit melodramatic and apocalyptic, but it's not too far for the truth. The era of post-peak oil is coming. And it's stands to change a lot of things. If you want a basic primer on Peak Oil, check out this article on Salon.com from today. It's a pretty well balanced look at the fate of fossil fuels in the US and the world.

What scares me most about all this is that the facts just don't seem to be out there for the public. Most geologists and economists (the people I'd think we should be listening to) seem to agree that in the next 10 to 50 years, oil will reach an all time high demand and low production and that this will have a drastic effect on the modern world. Yet, you don't see any of the major news stations covering this, any of the major newspapers printing it, or any of the leaders of the world realistically discussing it. Maybe it's not feel-good enough. 'Why tell people they shouldn't drive their gas-guzzling Hummers? That won't improve our ratings!'

My questions for everyone: how do you feel about all this? Do you think it's a big bunch of liberal propaganda to promote environmentalism, or is it for real (the science would seem to point in the latter direction)? How do you think it will effect your future? Do you think it will affect your future?

I for example, think this is a major oppurtunity for humanity to kick some major ass and take some giant leaps forward technologically. With breakthroughs in nanotechnology, humanity is very close to getting to the point that we can harness energy from the sun to directly hydrolize water, creating free hydrogen that can then be used as the "fossil fuel" of the future. That's the career path I most see myself in, so in a way, Peak Oil is involved in my future career prospects simply by coincidence. Go figure.

How about you?

A Manifesto (Or Something Like That)

Well, I see that this blog hasn't quite taken off like I'd hope. But Rome wasn't built in a day, and this blog is less than a week old. So, yes, there's still hope.

I thought I'd share with you my hopes for this website, and where I see it's purpose right now. First, the hopes. I hope that eventually this site takes on a life of it's own, with ideas cropping up, being taken to their extremes, stretched to capacity, therefore creating new topics, new solutions and new interests. Right now I see it like this: this site is a seedling. It needs a lot of TLC before it reaches critical mass and can start taking care of itself. When it does reach critical mass, it will essentially continue to grow organically, with little or no effort on anyones part. Until then, I guess I/We will have to act as careful stewards. Why? Because I don't especially want to see this site die before it gets that first shoot above ground.

Now to the purpose. First and foremost, I want this blog to be about having fun. I want the posters to enjoy what they're posting on, finding genuine interest in sharing their opinions and ideas on various issues. I want this blog to spark ideas, guide imagination, and create interests. Let's face it: each of us has a limitted area of interest and expertise, and we could all use a little help from the other experts out there. This site's a great place to test ideas, practice argumentaion and discourse. It's a great place to find out how others feel about different topics. On a slightly more serious note, this blog highlights some of the best and brightest in Chi, and therefore will give us some idea of what the future holds. Saying that, let's not get too uptight. This is, as I said before, should be FUN.

I'm going to start everything off with a post that I hope everyone will be interested in. Until we blog again,

David

PS - If you'd like an example of a collaborative blog, check out Generation Sit. This is basically the format I'm going for with Think Bowl. Of course, our topics can span any area of interest. Hopefully this will give you a general idea of what I had in mind.

A Blog is Born

Here it is, ladies and gentlemen, in all it's newborn glory. After careful consideration and a lot of planning (read little consideration and minimal planning), I decided to name this blog "Think Bowl," a play on the words "Think Tank." Maybe not so witty, but I thought "Think Tank" was rather dry.

Anyway, welcome to "Think Bowl: Thoughts in Chi." This blog was born of careful ruminating on my part here and here, in addition to a general desire to create some sort of "we" space that the people of Chichester (well, namely my friends for now) may come together and exchange/share ideas.

And there's the catch: this blog must be bigger than me in order for it to be a success. I have my own blog here, but that's only the self of the self, culture, nature trio that makes up life. In order to succeed, I need you, yes you, to join this blog and share with us your marvelous thoughts. Without that, this blog is nothing.

I really do hope that this blog manages to live on past me, or at least past my leaving Chi. I could think of no greater legacy of my Chichester education than to leave this blog forever on the internet to spark the minds of future Chichesterians, or Chichester Alumni (as many of us will be in only a few months) in years to come. I realize that's a tad grandiose (yeah, just a tad), but if you don't think big, you might as well not think at all.

As I said, you're needed to make this work. If you want to join this experiment, either e-mail me or leave a comment leaving your e-mail address. Then I can send you an invitation to join the "members" of this blog, allowing you to post to your hearts desire. And a word on posts: feel free to post on anything you desire, no matter what you think others might think of it / care of it. This is an arena for thoughts to flourish, not to flounder.

Thanks again for your time and attention. I hope you find this site useful, and even at times entertaining and enlightening.

Your Faithful Founder,
Dave Darmon