This morning on my way in to work, as with nearly every morning, I caught a great little piece on our local NPR public radio station called Engines of Our Ingenuity, presented by the University of Houston’s College of Engineering. These bits are very interesting, informative and educational, covering a wide variety of topics for all kinds of people...even non science/technology geeks like me. :)

Today, this particular piece was about numbers, but there is something very important nested within this piece that I want to highlight. For the sake of context, I'm presenting the full transcript of today's episode, and many more transcripts can be found here:

http://www.uh.edu/engines

I will highlight the parts I wish to focus on (and the reason for this post).

_________________

What do the following words have in common: natural, imaginary, real, irrational, and transcendental. If you guessed “states of mind,” you’re probably not alone. But the better answer is they’re types of numbers. We take numbers for granted. One, two, three. These are the natural, or whole numbers. What could be simpler? Fractions are no trouble. Half a cup of sugar, a quarter teaspoon of salt. These are called rational numbers because they can be written as the ratio of two whole numbers. But many numbers aren’t rational. We call them irrational.

One of the most famous irrational numbers is the square root of two. The Pythagoreans’ of ancient Greece discovered this fact. They were a mystic cult, living according to strict rules established by their leader, Pythagoras. Numbers were divine to the Pythagoreans. So when one of their own, Hippasus of Metapontum, discovered the square root of two was irrational, it upset their entire understanding of the world. Legend has it that Hippasus was killed for his heresy. Ironically, we now call the rational and irrational numbers taken together, the real numbers. When we add a number called i, representing the square root of negative one, we get the imaginary numbers. They’re perfectly good numbers, though they’d probably have caused the Pythagoreans to drink hemlock-laced Kool-Aid.

And things only get stranger. We know that the rational and irrational numbers are both infinite. But there are infinitely more irrationals than rationals. That’s because there’s more than one type of infinity. This is the result of Georg Cantor’s pioneering work on transfinite numbers. Cantor’s contemporaries were extremely critical of his efforts. Henri PoincarĂ© called Cantor’s transfinite numbers a “disease.” Leopold Kronecker, one of Cantor’s teachers, called Cantor a “scientific charlatan” and a “corrupter of youth.” Today, mathematics and engineering students can’t survive without knowing at least some of what Cantor unearthed.

Cantor’s work led him to study sets. The set of all red cars, the set of socks in the bottom drawer. Mathematicians believed sets were even more basic than numbers. So in the late nineteenth and early twentieth centuries they went about defining numbers using sets.

It seems crazy. Why fuss with sets? But it laid a foundation that helped us learn many surprising things about what we can and can’t do with mathematics. And … with computers. Today’s digital computers work with one thing, numbers. Peek inside and you’ll see everything expressed in numbers, from the icons on your desktop to the email waiting in your inbox. Numbers make our copiers copy, our phones phone, and our word processors process. We couldn’t do without them. Wonderful, practical, even divine numbers.

_________________

Now let's focus back on the highlighted part of this transcript. Throughout history revolutionary ideas have been scoffed at, ridiculed and rudely (if not violently) challenged. This is but one example, and many can be researched beyond just the sciences.

My point is that when people attack, ridicule, scoff and degrade "radical" ideas like the Venus Project, the Electric Universe, or people like Nassim Haramein, or conduct any other such action, remember that history is full of people who do this. They are the ones challenged, fearful, or simply too egotistical to accept something different.

In time, they are typically proved to be wrong at least to some degree, but I'm certain at the time they wielded great swords of superiority...at least in their own minds. :)

So remember that time based validation is the true test, and so is social and technical evolution.

Onwards and upwards, let not the baggage wielders of outdated thinking hold back the progress of mankind.

Today, this particular piece was about numbers, but there is something very important nested within this piece that I want to highlight. For the sake of context, I'm presenting the full transcript of today's episode, and many more transcripts can be found here:

http://www.uh.edu/engines

I will highlight the parts I wish to focus on (and the reason for this post).

_________________

What do the following words have in common: natural, imaginary, real, irrational, and transcendental. If you guessed “states of mind,” you’re probably not alone. But the better answer is they’re types of numbers. We take numbers for granted. One, two, three. These are the natural, or whole numbers. What could be simpler? Fractions are no trouble. Half a cup of sugar, a quarter teaspoon of salt. These are called rational numbers because they can be written as the ratio of two whole numbers. But many numbers aren’t rational. We call them irrational.

One of the most famous irrational numbers is the square root of two. The Pythagoreans’ of ancient Greece discovered this fact. They were a mystic cult, living according to strict rules established by their leader, Pythagoras. Numbers were divine to the Pythagoreans. So when one of their own, Hippasus of Metapontum, discovered the square root of two was irrational, it upset their entire understanding of the world. Legend has it that Hippasus was killed for his heresy. Ironically, we now call the rational and irrational numbers taken together, the real numbers. When we add a number called i, representing the square root of negative one, we get the imaginary numbers. They’re perfectly good numbers, though they’d probably have caused the Pythagoreans to drink hemlock-laced Kool-Aid.

And things only get stranger. We know that the rational and irrational numbers are both infinite. But there are infinitely more irrationals than rationals. That’s because there’s more than one type of infinity. This is the result of Georg Cantor’s pioneering work on transfinite numbers. Cantor’s contemporaries were extremely critical of his efforts. Henri PoincarĂ© called Cantor’s transfinite numbers a “disease.” Leopold Kronecker, one of Cantor’s teachers, called Cantor a “scientific charlatan” and a “corrupter of youth.” Today, mathematics and engineering students can’t survive without knowing at least some of what Cantor unearthed.

Cantor’s work led him to study sets. The set of all red cars, the set of socks in the bottom drawer. Mathematicians believed sets were even more basic than numbers. So in the late nineteenth and early twentieth centuries they went about defining numbers using sets.

It seems crazy. Why fuss with sets? But it laid a foundation that helped us learn many surprising things about what we can and can’t do with mathematics. And … with computers. Today’s digital computers work with one thing, numbers. Peek inside and you’ll see everything expressed in numbers, from the icons on your desktop to the email waiting in your inbox. Numbers make our copiers copy, our phones phone, and our word processors process. We couldn’t do without them. Wonderful, practical, even divine numbers.

_________________

Now let's focus back on the highlighted part of this transcript. Throughout history revolutionary ideas have been scoffed at, ridiculed and rudely (if not violently) challenged. This is but one example, and many can be researched beyond just the sciences.

My point is that when people attack, ridicule, scoff and degrade "radical" ideas like the Venus Project, the Electric Universe, or people like Nassim Haramein, or conduct any other such action, remember that history is full of people who do this. They are the ones challenged, fearful, or simply too egotistical to accept something different.

In time, they are typically proved to be wrong at least to some degree, but I'm certain at the time they wielded great swords of superiority...at least in their own minds. :)

So remember that time based validation is the true test, and so is social and technical evolution.

Onwards and upwards, let not the baggage wielders of outdated thinking hold back the progress of mankind.

## 2 comments:

I think, at the very least, it is important to challenge the status quo, if for nothing else, to have it prove itself as the "way things should be". To let ideas and visions of what the "world should be" go unchallenged is not only counter-productive, but downright dangerous. And to be fair, those who challenge the status quo with esoteric ideas must obviously be challenged as well, if not more so.

I might go as far as to say that those who play the game of new ideas would be disappointed if they weren't ridiculed or dismissed. The rejection may be integral to motivation.

Thus why I like science so much, if practiced properly. It's designed to constantly poke at itself, either reinforcing current "truth for the moment" or breaking it and finding a better "truth for the moment". Either way, it's a bonus for knowledge gain or reinforcement.

This is why I can't stand profit motives leaking into science, because after all, funding is a profit motivated scheme for most cases.

As for ridicule being a motivator, I do agree with that. That weeds out the posers vs. those who have strong conviction in what they believe to be true...as long as they can back up their claims with data and sound science that is. lol.

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