Just wanted to point out the mathematics of reducing the plate size from 12" to 10".

Measuring my own plates (which are 10") I noticed that the border for the plates is approx 1.5" wide, which reduces the effective area of the plate by 3" diameter.

A 10" plate will have a 7" effective diameter, and using pi*r^2 we have an area of approx 154.

A 12" plate would have a 9" effective diameter, and calculating it's area we get approx 254.

A 10" plate is 40% smaller in effective area than a 12" plate, so to me it's actually surprising that there is only a 22% reduction in food consumption (which can probably be explained by the psychology of perceived portion sizes and wanting to fill in the empty space of a plate).

You know what would convince me that what I think is a square is in fact a circle (55:58)?

Give me a mathematical model for both of them. Then do a fit (least squares?) to both models.

If it turns out that the circle is a better fit - then it's clearly a circle.

>> ^KnivesOut:

This reminds me of the logic behind the Klein bottle. It's the allowance for intersections that makes it "possible".


Yeah they kind of lost my interest at that point as well. I guess if you're working with theoretical mathematics, it's acceptable to consider theoretical materials too...

Ayn Rand's Influence on Alan Greenspan
In The Age of Turbulence, Alan Greenspan describes the influence that Ayn Rand had on his intellectual development.

Ayn Rand became a stabilizing force in my life. It hadn't taken long for us to have a meeting of the minds -- mostly my mind meeting hers -- and in the fifties and early sixties I became a regular at the weekly gatherings at her apartment. She was a wholly original thinker, sharply analytical, strong-willed, highly principled, and very insistent on rationality as the highest value. In that regard, our values were congruent -- we agreed on the importance of mathematics and intellectual rigor.

But she had gone far beyond that, thinking more broadly than I had ever dared. She was a devoted Aristotelian -- the central idea being that there exists an objective reality that is separate from consciousness and capable of being known. Thus she called her philosophy objectivism. And she applied key tenets of Aristotelian ethics -- namely, that individuals have innate nobility and that the highest duty of every individual is to flourish by realizing that potential. Exploring ideas with her was a remarkable course in logic and epistemology. I was able to keep up with her most of the time.

Rand's Collective became my first social circle outside the university and the economics profession. I engaged in the all-night debates and wrote spirited commentary for her newsletter with the fervor of a young acolyte drawn to a whole new set of ideas. Like any new convert, I tended to frame the concepts in their starkest, simplest terms. Most everyone sees the simple outline of an idea before complexity and qualification set in. If we didn't, there would be nothing to qualify, nothing to learn. It was only as contradictions inherent in my new notions began to emerge that the fervor receded.

One contradiction I found particularly enlightening. According to objectivist precepts, taxation was immoral because it allowed for government appropriation of private property by force. Yet if taxation was wrong, how could you reliably finance the essential functions of government, including the protection of individuals' rights through police power? The Randian answer, that those who rationally saw the need for government would contribute voluntarily, was inadequate. People have free will; suppose they refused?

I still found the broader philosophy of unfettered market competition compelling, as I do to this day, but I reluctantly began to realize that if there were qualifications to my intellectual edifice, I couldn't argue that others should readily accept it. [...]

Ayn Rand and I remained close until she died in 1982, and I'm grateful for the influence she had on my life. I was intellectually limited until I met her. All of my work had been empirical and numbers-based, never values-oriented. I was a talented technician, but that was all. My logical positivism had discounted history and literature -- if you'd asked me whether Chaucer was worth reading, I'd have said, "Don't bother." Rand persuaded me to look at human beings, their values, how they work, what they do and why they do it, and how they think and why they think. This broadened my horizons far beyond the models of economics I'd learned. I began to study how societies form and how cultures behave, and to realize that economics and forecasting depend on such knowledge -- different cultures grow and create material wealth in profoundly different ways. All of this started for me with Ayn Rand. She introduced me to a vast realm from which I'd shut myself off.

From The Age of Turbulence, pp. 51-53. Omissions from the text are shown with bracketed ellipses. All other punctuation and spelling is from the original.

http://www.noblesoul.com/orc/bio/turbulence.html

Interesting, but I really dislike the Drake equation. First, it doesn't really tell you anything; so many of the "variables" are unknown, arguably un-knowable, or overly broad generalizations that it makes the whole thing rather pointless. There is nothing mathematically intelligent about it. When so many of the factors are things that we can't even really take an honest guess at, you might as well say "N = N". Instead, it tries to work backwards and just overly complicates the whole mess.

Second, a whole bunch of it is based on things that are, in my opinion, false premises. In fact, you could provide reasonably solid arguments against the relevance of every single factor/variable.

Take the first 3: how many stars are there, how many have planets, and what percentage of those planets are habitable. Why must life come from planets? We've discovered life on Earth in thermal vents with temperatures in multiple hundreds of degrees C, frozen layers well below zero C, places with no light, oxygen, etc. etc. Who's to say that other things that are recognizably alive couldn't exist in other environments that seem "extreme" to us, outside of a planetary setting?

fl, fi, and fc are all things that would require us to exhaustively search every single planet in the galaxy, not just across space but across time as well, to really "know". If we could do that, then we could just give a direct answer for N to begin with. Seems pointless.

>> ^MycroftHomlz:

Mechanical Engineering isn't science!


By that reasoning neither is a degree in mathematics.

Really it is a degree entirely based on and drenched in science. There is no guess work. If you need to find out something new you make a hypothesis, run some tests, get some results, validate the hypothesis, etc. all to the scientific method.

finding the new mass within 4.9 standard deviations is using a huge amount of work on the precision of the tool, thus the necessity for such large equipment. The key for even laymen here is to understand the concept of standard deviations, something you will find in a finite mathematics course and statistic courses. quite impressive!

http://en.wikipedia.org/wiki/Standard_deviation

ps Dr Hawking is so god damn charming lol!!! what a guy

I don't think there is any complex mathematical explanation. Given a starting point of 52 cards and as you point out the fact that the order of the remaining cards is reversed on each pass to keep the aces in even numbered positions, as long as the aces start in the 6th, 22nd and 38th positions you'll get the desired result. This will still work if the first pile has a different number of cards as long as the number moved top to bottom at the end combined with the first pile totals 14.

You really haven't been paying attention if you think I'm not open to the idea of a god @shinyblurry. The very fact that I'm arguing I don't know, directly implies that I'm an agnostic, not an atheist.

I've seen that you have an openness to the idea, but you're also quick to take an adversarial position. Are you truly open to who God is? Are you okay with the idea of a God so long as it isn't Jesus?

I can also say that as a former agnostic, I understand where you're coming from.

There could be a god. But 1) there has to be proof of the it's existence

Logically, if there is a God, the entire Universe is proof of His existence. I don't know about you, but personally I find the idea of Universes spontaneously creating themselves to be an absurdity.

Imagine a painting with three black lines on it. You could come to all sorts of conclusions about what that is supposed to represent. You could draw philosophical ideas from it. You could see it as a social commentary, or a mathematical representation. You could measure it, sample the paint and paper, run many different tests. You could count the number of brushstrokes. You could do all of this and more, subject it to every sort of empirical inquiry, and you would be no closer to finding about the intention of the painter than you were when you started.

The only way you are going to see the signature of the Creator is if you realize you are looking at His Creation. The evidence is *everywhere*. Neither is poking and prodding it and subjecting it to tests going to tell you anything about what He intended. This is the only real question.

and 2) Religion and god are two separate things, just because a creator exists doesn't give any more credibility to religion.

I agree, and I've made this point to atheists in the past, mainly when I believed that no religion was the correct one. If you consider that everything is equally unlikely, then you are looking at 50/50 odds for special creation versus naturalistic means.

There are many many religions out there. Assuming one is right, that means many are wrong More than likely, all are wrong.

Why is it more likely that all are wrong rather than one being right? The question is, has God revealed Himself to the world, or not. If not, then all are wrong. If so, then one is right.

In all likelihood, odds are better that a creator would be more like Cthulhu then some caucasian, gun loving republican. You claim god made us in his image, when in reality, it's far more likely that you made god in our image.

The stereotype you are presenting does not represent anything Christians believe. Maybe some Christians act that way, but that isn't what scripture says about God. It says that as the Heavens are higher than the Earth, so are His ways above our ways.

If we were created, humans are the Creators crowning achievement. The "odds" are better that He made us like Him.

The simple truth though is that god is academic. Either he's always been here and it's all part of some ridiculously elaborate pre-destination plan so it doesn't matter what we do as it's all part of the plan, or he doesn't care, or he does, but he doesn't intervene. In each of those cases. The alleged fact of a creator's existence does not affect our lives, at least not any way we're aware of. Nor does a creator suddenly make any of the religions right or true.

Or, it does matter what we do, because God does intervene in His creation, and He has given us a standard of behavior which He is going to judge us by. The existence of God does not make any of the religions true, but it is positive evidence that one of them is true.

Or god doesn't exist and never has. Again...nothing changes. religion still exists in spite of this, they still get together and do their thing and that's fine. Religion is not inherently bad, it's what you DO with religion that is hurtful or helpful. Even if you removed religion from humanity forever. Humanity still has a ton of other things that we do that are part of our lives that have no rational basis in fact but we do it anyway. That's fine...it's part of what makes us human.

Man corrupts everything he touches because our nature is inherently sinful. Man can use anything as an excuse to do evil.

The dilemma is not for me to believe, the dilemma is for you and/or your god to prove why I should believe. Especially if you want public policy to be influenced. When public policy is not involved, you have the same freedoms everyone else does. And you can't use the bible to prove you're right. You do know what circular reasoning is and that' it's a fallacy right? You quoting the bible does absolutely nothing other than to show you don't really understand what reasoning and logic is.

http://en.wikipedia.org/wiki/Circular_reasoning

Except there is evidence in the bible which proves the bible is Gods word, such as the fulfilled prophecy. It may not prove that I am right, to you, but the evidence has convinced over 1/3 of the worlds population. That isn't even the question, in any case. I'm not trying to prove I am right to you. I don't believe there is anything I can do to ever convince you that God exists, or that His name is Jesus Christ. That's the work of the Holy Spirit.

That is what I was explaining to you earlier. It's not an evidence problem, it's a heart problem. God has already given you sufficient evidence to know that He is, and who He is. Only God can change your heart. What He charged me with is to tell you the gospel and give you an answer for the faith that I have.

Religion wants to say they're right and everyone else is wrong. That's nice. A lot of people think they're right and everyone else is wrong. I think I'm right and my supervisor is wrong. The onus is on me to show why I'm right.

I'm glad you've found happiness in your religion. I've found happiness in the way I live which does not require a god or a religion. Who is right? Maybe none of us are right. Maybe we both are right. The lesson is just simply that there are many ways to happiness. There is no single way. Your happiness is not better than my happiness and vice versa. Your happiness does not get to infringe on my happiness and vice versa. This is how we live and get along in the great melting pot. You don't get dominion. you never will. History is quite clear on what happens when a group of people come along and say, live our way..or else. Believe in the same things we believe...or else.

Christians are not called to have dominion. I will of course strongly disagree with immoral laws, but people have the right to govern themselves as they wish. Although this is still a strongly Christian nation, we have a strong secular influence in our government. I accept that as being the reality.

your happiness does not get to trump someone else's happiness. If you let people steal and kill you have a lot of unhappy, and dead people. That's not sustainable and you can't really survive that way. Again, simple morality that does not require a creator. Next question?


You said that it isn't sustainable yet if you look at history you will see that stealing and killing is what we have been doing all along. The point is this..Let's say that the Nazis won the war and conquered the world. Eventually, they won everyone over to their philosophy, and now there is peace on the Earth. The glue that holds everything together is that once a year, they torture a jewish baby to death on camera, which brings great happiness and unity to the entire world. One year the baby died before they could torture it, and there were riots and many, many people were killed. Is it therefore moral to torture that baby to death, since it brings peace and happiness to the entire world?

>> ^VoodooV

Hmm. Never really thought about it before. The english way always made more sense to me, because it's what I was taught so anything else would seem wonky. But this video has changed my mind. I'm a big fan of mathematical elegance and this video has now ruined my interactions with large numbers

I love how much this guy loves the mathematical progression of the language.

These are pretty pansy little numbers; sure they're kind of long, but they're computable. We know digits of this number.

If you want truly large numbers, you want to use the Busy beaver function. These are numbers for which we can say beautiful, absolute things like:

in the context of ordinary mathematics, neither the value nor any upper-bound of Σ(10↑↑10) can be proven


That is a majestic bloody number.

@NetRunner, you wrote: "In other words, you don't dispute that women are being paid less as a group, you just believe that this is because women as a group aren't doing equal work. They stay at home to raise children, don't pursue advanced degrees, or maybe they just weren't raised to be as outspoken/competitive/aggressive as men. Whatever the cause, you posit that it is this deficit in quality or quantity of work from women which is the primary reason women get paid less than men on average. That's not a basic agreement with A, that's a wholly different assertion."

>>>Actually, that's not my argument. There is a disparity between the ways in which men and women are expected to contribute value to the society and this disparity is reflected, generally speaking, in the kinds of jobs that are sought/provided, responsibilities that are sought/provided, and roles or identities that are sought/provided by and for the genders. This is a distinction from lifestyle choice, which is not as socio-culturally pernicious as what I'm attempting to convey. However, if you are suggesting that I disagree with PL for EW, you're only partially correct. There are statistics by which the disparity in wages could be held in the light of (stats which are outside the scope of my work-week to specifically cite here), which indicate, for example, that men are more likely to spend more time away from the families than women, more years of their lives in careers than women, more involved with physically debilitating occupations than women, more likely to be sent to (and die in) wars than women, more likely to be held financially liable for the support of children with or without legal custody, etc. What I am suggesting is that while each of these taken individually might be considered an "lifestyle choice," as a whole, they are part of a much larger underlying societal expectation which then holds men accountable if they are unable to serve their male function as "providers" or "protectors."
As I asked before, what value is lost by the wage disparity?

@NetRunner, you wrote: And yes, I get that you're saying it in a soft, non-accusatory tone -- it's not that women are intrinsically inferior, it's that our society as a whole is shaping them into less valuable workers, whether they want that or not.

>>>Closer. The society is also shaping men into 'wage earners' whether they want that or not.


@NetRunner: Still, I think anytime you go around saying pay discrimination is in any sense justified, you're wading into some dangerously misogynistic waters. Worse, I think if you use the word "myth" to describe the idea that women face unjust pay discrimination, you've pretty much jumped in with both feet.

>>>Show me where I have posited that the pay discrimination is justified! I will immediately retract it. There are ingrained habits of this argument into which you seem to want to place me, but that is not the position I am taking. It is, by no means, a "myth," that women get paid less than men for equal work. That much is mathematically accurate. What is "mythical" about it is that circumstances under which that wage disparity exists is identical between the genders. It is not, but is instead indicative of a much larger, deeper, societal disparity between the genders... one that did/does not get adequate attention.

So how many blueberries could fit in the Earth? Trillions? Quadrillions? It's now my mission to figure out the maths for that....

Ok, so I suck at mathematics but I was way off. The volume of Earth is already 10 to the power of 21 cubic meters. Multiply that by 500,000 or however may berries in a cubic meter and what's that like five hundred thousand trillion quadrillion atoms in a grapefruit. Mind = blown