Calculus Made Easy, 1910: All the little bits

Calculus Made Easy is a book on introductory calculus originally written in 1910 by Silvanus P. Thompson. It was such a well-received text for teaching calculus, that it can still be found in print today (it's now in the public domain and also freely available online).

The first bit of text from the first chapter is fairly intriguing. So much so, that I thought you might like to read it here:

Thinking of the integral of dx as an easy way of saying "the sum of all the little bits of x" is a really intriguing approach to explaining some of the most basic ideas of calculus. 

If you've struggled at all with learning calculus, then you may want to give Calculus Made Easy a read. It may be over 100 years old, but much of the writing is still of great value for the interested student.

Raising Some Funds for the Humane Society

My husky Darwin is decked out in some Humane Society of Boulder Valley gear in this picture for the upcoming Doggie Dash 2018! 

The huskies are raising some moolah to support our local Humane Society. If you have a moment and might be able to give, check out the fundraiser at this link:

Help the huskies raise money

for the Humane Society of Boulder Valley!

Love these silly doggos!

From Mike Rowe Regarding the Fake Hurricane Reporting

By now you've probably seen (or at least heard of) the video of Weather Channel correspondent Mike Seidel in Wilmington, North Carolina, trying to "fight heavy winds" of Hurricane Florence as he reported live on Friday, only to shortly after have the camera catch two people walking behind him with no troubles with the wind at all. The video is yet another reminder that we can't necessarily trust what we see in the media and a sign of bogus journalism. I just came across Mike Rowe's comments regarding the clip and thought I'd share them here:


"Gale-Farce Winds!!!

Typically, I don't share videos that have already been viewed millions of times. Feels like old news. But old news is better than fake news, and here, we have an example of fake news so perfectly personified I can't help but bring it to your attention.

Watch this clip. Ironically, it's one of the most honest things I've seen in a long time. But not because The Weather Channel is committed to honesty. No, the truth here is accidental, and comes courtesy of the people in the background. Two guys, casually strolling through what the reporter would have us believe are gale force winds.

Or "gale-farce," if you will.

This is the problem with television today. No one can tell the difference between a commercial and a documentary. There's no line between reality and non-fiction, news and entertainment, or in this case, a weather report and a skit on SNL. No one knows whom to trust anymore, because the landscape is littered with hosts and reporters and correspondents so desperate to hold our attention that they'll do or say anything. And still, in the midst of so much pretense and pandering, they beg us to trust them! They literally beg us, with a level of earnestness that defies credulity. And then, they pretend. They perform. They act.

Do yourself a favor - if you're looking for the truth, look behind the scenes. That's where authenticity lives. That's why I've always insisted on hiring a behind-the-scenes camera to document every show I've ever worked on. That's why I'm insistent about incorporating that footage into whatever makes it on the air. Because it shows the truth, in a far more persuasive way than I could ever describe it.

Travis McGee, my favorite fictional character, once said, "Be wary of all earnestness." He was right. Earnestness and truth have nothing to do with one another. Consider that the next time you see a news story or a weather report that's preceded by a lurid graphic, dramatic music, and urgent sounding narration, and then ask yourself if the network is trying to inform you, or simply keep you from turning the channel. And remember this too - if a network or a reporter or the host of non-fiction TV show is asking for your trust, it's only because they're too lazy to earn it.

Be wary of all earnestness..."


You can watch the video here:

Co-Hosting Ask an Astrobiologist!

I’ve recently agreed to become a co-host of the show Ask an Astrobiologist! 

Ask an Astrobiologist, brought to you from the community of SAGANet, is a NASA Astrobiology-sponsored show that airs online once each month. In each episode, either myself or Sanjoy Som will interview a guest astrobiologist to ask about their career paths, their scientific research, and the things that drive them to wonder about the nature of life in the universe. Every episode also features a photo contest with the potential to win some NASA swag!

Ask an Astrobiologist airs live on SAGANet and on the NASA Astrobiology Facebook page. People watching the show live can ask questions of our interviewees on either streaming platform or on Twitter using #AskAstrobio. 

I’m definitely excited for becoming more involved with the show! Look for more here in the future, including episodes and my personal comments about what it's like to host a show like this!

An emoji puzzle that takes a little integral calculus to answer

You may have seen some of the emoji puzzles that make their way around Facebook and other social media sites. Usually they require that you do some simple algebra (like adding 3 monkey emojis equal the number 15, so what number is one emoji monkey representative of?), but I just saw this little gem that actually required a little bit of fun ol' integral calculus. Give it a look-see:

What do you think? Does it look like fun? Give it a go and then I'll post the answer below.






















Okay, let's talk about the answer to this fun little puzzle. It starts off pretty easy, just using a little bit of algebra. The first part gives us three bottles of beer added together to equal 30. Easy enough, right? Each bottle must represent the number 10:

After that, we get to mix our beer bottle variable with a new variable, a cheeseburger! Again, pretty easy math. The cheeseburger must represent the number 5:

And then, again, we get to use the variable from the last bit to workout the next part of the problem, where we find that two glasses of foaming ginger beer (hey, it can be whatever you want it to be, really) will represent the number 2:

But after that, things get a little harder. Now we have the following integral:

We can start by plugging in the stuff we already have (in this case, our beer bottle, cheeseburger, and glasses of foaming ginger beer variables). That yields:

Which then can be rewritten as:

If you haven't had much experience with integral calculus, that expression above probably still looks pretty confusing. If this is the case, then you might want to check out Khan Academy's lessons on integral calculus, since that'll give you a good leg up on how this type of math works. But, assuming you already have some experience with integral calculus, you might notice that the above expression is very similar to the improper integral of the sinc function over the positive real numbers. This kind of function actually has a specific name and a well known solution. It's called a Dirichlet Integral, and, in this case, has a solution of pi over 2:

So, if we solve the same way using our previous expression from the problem at hand, we get:

So the answer to the original problem is numerically 5pi/2. But we started off with a mix of emojis and numbers, so why not go back to emojis. We already have emojis for 5 and 2 (cheeseburger and two frosty glasses of ginger beer, respectively), but we need one for the number pi (which is usually represented by the Greek lower case letter). Why not use pie?! We then get a final answer of:

And that makes the problem even more fun! Now I think I'll go enjoy a cheeseburger and some ginger beer and follow up with a little pie. Cheers!

John McCain's Farewell Statement

Senator John McCain died this past week. He was 81 years old. There was once a time when I was younger where I would say openly that if John McCain ran for President, then I was likely to vote for him. Sadly, his presidential campaign in 2008 became overrun by the idiocy of far right conservative politics in America. Adding Sarah Palin to the campaign and paying lip service to the fundamentalist right definitely weakened the campaign. Yet, there were still powerful McCain moments. The "No Ma'am Moment", when McCain responded articulately and strongly to a woman who claimed Obama was an Arab and she couldn't trust him, will probably be the best-remembered moment of his presidential run. Yet, his farewell statement, released to the American public following his death, may one day be his best remembered statement, especially as the words are poignant and meaningful at a time when the Trump Administration, xenophobia, and extremism (on both sides) are threatening the future of American democracy. I've copied the words of the statement below, for anyone interested in reading them. The bold highlights of the text are mine, but, truly, all the words are those of the now deceased Senator John McCain.

2008 presidential candidate John McCain, before a rally in Cedar Falls, Iowa (Oct. 26, 2008; AP Photo/Carolyn Kaster)

"My fellow Americans, whom I have gratefully served for sixty years, and especially my fellow Arizonans,

Thank you for the privilege of serving you and for the rewarding life that service in uniform and in public office has allowed me to lead. I have tried to serve our country honorably. I have made mistakes, but I hope my love for America will be weighed favorably against them.

I have often observed that I am the luckiest person on earth. I feel that way even now as I prepare for the end of my life. I have loved my life, all of it. I have had experiences, adventures and friendships enough for ten satisfying lives, and I am so thankful. Like most people, I have regrets. But I would not trade a day of my life, in good or bad times, for the best day of anyone else's.

I owe that satisfaction to the love of my family. No man ever had a more loving wife or children he was prouder of than I am of mine. And I owe it to America. To be connected to America's causes -- liberty, equal justice, respect for the dignity of all people -- brings happiness more sublime than life's fleeting pleasures. Our identities and sense of worth are not circumscribed but enlarged by serving good causes bigger than ourselves.

'Fellow Americans' -- that association has meant more to me than any other. I lived and died a proud American. We are citizens of the world's greatest republic, a nation of ideals, not blood and soil. We are blessed and are a blessing to humanity when we uphold and advance those ideals at home and in the world. We have helped liberate more people from tyranny and poverty than ever before in history. We have acquired great wealth and power in the process.

We weaken our greatness when we confuse our patriotism with tribal rivalries that have sown resentment and hatred and violence in all the corners of the globe. We weaken it when we hide behind walls, rather than tear them down, when we doubt the power of our ideals, rather than trust them to be the great force for change they have always been.

We are three-hundred-and-twenty-five million opinionated, vociferous individuals. We argue and compete and sometimes even vilify each other in our raucous public debates. But we have always had so much more in common with each other than in disagreement. If only we remember that and give each other the benefit of the presumption that we all love our country we will get through these challenging times. We will come through them stronger than before. We always do.

Ten years ago, I had the privilege to concede defeat in the election for president. I want to end my farewell to you with the heartfelt faith in Americans that I felt so powerfully that evening.

I feel it powerfully still.

Do not despair of our present difficulties but believe always in the promise and greatness of America, because nothing is inevitable here. Americans never quit. We never surrender. We never hide from history. We make history.

Farewell, fellow Americans. God bless you, and God bless America."

Augeries of Westworld Innocence

Nebuchadnezzar, William Blake (c. 1805)

We're just now getting around to finishing Westworld Season 2 (it's been a pretty busy summer). One striking scene for me in this season of the show was a simple little scene where the character of Ford (Anthony Hopkins) is reintroduced, this time as a digital representation of himself within the control unit of Bernard (Jeffrey Wright). Not only is this a scene where Ford reveals rather eloquently that Westworld itself was an attempt to digitalize human consciousness and reach immortality as a species, but it's prefaced by Ford reciting these poignant four lines from Augeries of Innocence, by William Blake:

        To see a world in a grain of sand
        And a heaven in a wild flower,
        Hold infinity in the palm of your hand,
        And eternity in an hour.

Here's the scene itself in video:

This has long been one of my favorite lines from poetry, but the episode forced me to think a little more about the poem and how apt it is to the concepts considered in the show. Augeries of Innocence presents good and evil, right and wrong, etc. in light of natural and supernatural understandings of Blake's time. In many ways, the ideas touched upon in Westworld make us question good and evil and right and wrong when it comes to our development of modern technology (especially technology that not only has the potential to radically change who and what we are, but even to utterly destroy us). The episode has definitely had me thinking about this poem. Here's the entire poem, for your reading pleasure:

To see a World in a Grain of Sand 
And a Heaven in a Wild Flower 
Hold Infinity in the palm of your hand 
And Eternity in an hour
A Robin Red breast in a Cage 
Puts all Heaven in a Rage 
A Dove house filld with Doves & Pigeons 
Shudders Hell thr' all its regions 
A dog starvd at his Masters Gate 
Predicts the ruin of the State 
A Horse misusd upon the Road 
Calls to Heaven for Human blood 
Each outcry of the hunted Hare 
A fibre from the Brain does tear 
A Skylark wounded in the wing 
A Cherubim does cease to sing 
The Game Cock clipd & armd for fight 
Does the Rising Sun affright 
Every Wolfs & Lions howl 
Raises from Hell a Human Soul 
The wild deer, wandring here & there 
Keeps the Human Soul from Care 
The Lamb misusd breeds Public Strife 
And yet forgives the Butchers knife 
The Bat that flits at close of Eve 
Has left the Brain that wont Believe
The Owl that calls upon the Night 
Speaks the Unbelievers fright
He who shall hurt the little Wren 
Shall never be belovd by Men 
He who the Ox to wrath has movd 
Shall never be by Woman lovd
The wanton Boy that kills the Fly 
Shall feel the Spiders enmity 
He who torments the Chafers Sprite 
Weaves a Bower in endless Night 
The Catterpiller on the Leaf 
Repeats to thee thy Mothers grief 
Kill not the Moth nor Butterfly 
For the Last Judgment draweth nigh 
He who shall train the Horse to War 
Shall never pass the Polar Bar 
The Beggars Dog & Widows Cat 
Feed them & thou wilt grow fat 
The Gnat that sings his Summers Song 
Poison gets from Slanders tongue 
The poison of the Snake & Newt 
Is the sweat of Envys Foot 
The poison of the Honey Bee 
Is the Artists Jealousy
The Princes Robes & Beggars Rags 
Are Toadstools on the Misers Bags 
A Truth thats told with bad intent 
Beats all the Lies you can invent 
It is right it should be so 
Man was made for Joy & Woe 
And when this we rightly know 
Thro the World we safely go 
Joy & Woe are woven fine 
A Clothing for the soul divine 
Under every grief & pine 
Runs a joy with silken twine 
The Babe is more than swadling Bands
Throughout all these Human Lands 
Tools were made & Born were hands 
Every Farmer Understands
Every Tear from Every Eye 
Becomes a Babe in Eternity 
This is caught by Females bright 
And returnd to its own delight 
The Bleat the Bark Bellow & Roar 
Are Waves that Beat on Heavens Shore 
The Babe that weeps the Rod beneath 
Writes Revenge in realms of Death 
The Beggars Rags fluttering in Air
Does to Rags the Heavens tear 
The Soldier armd with Sword & Gun 
Palsied strikes the Summers Sun
The poor Mans Farthing is worth more 
Than all the Gold on Africs Shore
One Mite wrung from the Labrers hands 
Shall buy & sell the Misers Lands 
Or if protected from on high 
Does that whole Nation sell & buy 
He who mocks the Infants Faith 
Shall be mockd in Age & Death 
He who shall teach the Child to Doubt 
The rotting Grave shall neer get out 
He who respects the Infants faith 
Triumphs over Hell & Death 
The Childs Toys & the Old Mans Reasons 
Are the Fruits of the Two seasons 
The Questioner who sits so sly 
Shall never know how to Reply 
He who replies to words of Doubt 
Doth put the Light of Knowledge out 
The Strongest Poison ever known 
Came from Caesars Laurel Crown 
Nought can Deform the Human Race 
Like to the Armours iron brace 
When Gold & Gems adorn the Plow 
To peaceful Arts shall Envy Bow 
A Riddle or the Crickets Cry 
Is to Doubt a fit Reply 
The Emmets Inch & Eagles Mile 
Make Lame Philosophy to smile 
He who Doubts from what he sees 
Will neer Believe do what you Please 
If the Sun & Moon should Doubt 
Theyd immediately Go out 
To be in a Passion you Good may Do 
But no Good if a Passion is in you 
The Whore & Gambler by the State 
Licencd build that Nations Fate 
The Harlots cry from Street to Street 
Shall weave Old Englands winding Sheet 
The Winners Shout the Losers Curse 
Dance before dead Englands Hearse 
Every Night & every Morn 
Some to Misery are Born 
Every Morn and every Night 
Some are Born to sweet delight 
Some are Born to sweet delight 
Some are Born to Endless Night 
We are led to Believe a Lie 
When we see not Thro the Eye 
Which was Born in a Night to perish in a Night 
When the Soul Slept in Beams of Light 
God Appears & God is Light 
To those poor Souls who dwell in Night 
But does a Human Form Display 
To those who Dwell in Realms of day

New Graphics for One Flag in Space

One Flag in Space (OFiS) is one of the initiatives of Blue Marble Space, the non-profit that I work for. OFiS has a mission to inspire people to explore as citizens of Earth, using the Earth Day Flag as a symbol to represent all of humanity engaging in the act of space exploration and coming to better know our own world together. I recently put together some more graphics for sharing on our social media profiles. I thought I'd share some here as well. Enjoy!

Carbon Based Lifeforms Live at Ozora Festival 2017

Here's something blissful for your daily flow. A couple hours of Carbon Based Lifeforms, playing at the Ozora Festival last year in Hungary. I can't embed the video, so you'll have to scurry over to Youtube to watch it. But it'll be worth it. Trust me... I'm a doctor (Okay, not that kind of doctor, but still a kind of doctor). Here's a link to the groovy sounds (get 'em while they're contained within the massive information rich network of the interwebs!):

Carbon Based Lifeforms at Ozora Festival

Data & Picard by Pogo

Ah, some days I wake upon this world and find myself in a funk of uncertainty and overcome with the unrelenting bafflement of a society full of trite opinions and intellectually simple considerations of mostly insignificant things. But, then, there are days when the awesome sauce is flowing freely in the world and something like this gem falls into my life. Friends, fans, and fellow Star Trek lovers, "Data & Picard" by Pogo is here to make your day:

Was that good for you? I hope so. Want to learn more about Pogo (Nick Bertke)? Check out these links for more:

Website   Bandcamp   Twitter

Cheers folks. Go forth and do your good works!

A Sandworm Size Chart!

Now this is just too cool! I've been re-reading the Dune series again, so I suppose I've had sandworms on the brain lately. Admittedly, this "size chart" isn't even remotely to scale (that Dune sandworm would be a very small individual), but it's still pretty awesome. Maybe if I can find some time soon, I'll make an improved version myself! Until then, enjoy:

Looking Back Upon Me

I looked into the eye of the divine, 

   Driven.

That flaming jewel in the depths of the cosmos,

Set amid a blanket of starry darkness,

   Vast and beautiful.

I looked out to see where I fit,
And found the universe looking back upon me.

#ToExploreIsHuman

The blue lines in this image are parallel!

Mojave Crater, Mars

Within the Xanthe Terra region of Mars lies an impact crater known as Mojave (named after the town and desert in California!). The beautiful video below was put together by Seán Doran and shows a virtual flyover of Mojave Crater based on data from the HiRISE (High Resolution Imaging Science Experiment) instrument on the Mars Reconnaissance Orbiter (MRO). HiRISE has given us 12 years of incredible data, and the flyover video below is definitely a beautiful way to look at some of those data: