George Dyson, Turing's Cathedral: The Origins of the Digital Universe (New York: Pantheon Books, 2012), ix.

four big questions

the spring of 1787.

albums produced between 1908 and 1913 by developers and the real estate industry to entice potential middle and upper class tenants to New York City’s “principal high class apartment houses,” declares one volume’s subtitle. Each featured apartment house is briefly described, and illustrated with an exterior photograph and one or more floor plans.

Maria Anna (called Marianne and nicknamed Nannerl) was – like her younger brother – a child prodigy. The children toured most of Europe (including an 18-month stay in London in 1764-5) performing together as “wunderkinder”. There are contemporaneous reviews praising Nannerl, and she was even billed first. Until she turned 18. A little girl could perform and tour, but a woman doing so risked her reputation.

The effects of slavery endured long after emancipation.

Yet the end of legal slavery did not mean the end of racial injustice.

Lincoln won twenty-two states, and McClellan only managed to carry three: New Jersey, Delaware, and Kentucky.19

In a time when the average woman gave birth to eight to ten children in her lifetime,

In the North, the conditions in hospitals were somewhat superior. 

It is a common misconception that amputation was accompanied without anesthesia and against a patient’s wishes.

Around 1862 both armies began to dig latrines rather than rely upon the local waterways.

Tuberculosis, measles, rheumatism, typhoid, malaria, and smallpox spread almost unchecked among the armies.

arrested all rebellious women as prostitutes.

The working class citizens of New York felt especially angered as wealthy New Yorkers paid $300 for substitutes, sparing themselves from the hardships of war.

The Gettysburg Campaign was Lee’s final northern incursion and the Battle of Gettysburg remains the bloodiest battle of the war, and in American history, with 51,000 casualties.

There was never any doubt that black laborers and camp servants were property.

Gooding argued that, because he and his brethren were born in the United States and selflessly left their private lives and to enter the army, they should be treated “as American SOLDIERS, not as menial hirelings.

African American soldiers in the Union army endured rampant discrimination and earned less pay than white soldiers, while also facing the possibility of being murdered or sold into slavery if captured by Confederate forces.

In order to avoid the issue of the slaves’ freedom, Butler reasoned that runaway slaves were “contraband of war,” and he had as much a right to seize them as he did to seize enemy horses or cannons

. War meant the possibility of disruption to their cotton produced on the backs of slave labor, and disruption could have catastrophic ramifications in commercial and financial markets abroad.

“I think to lose Kentucky is nearly the same as to lose the whole game.

. Like an anaconda snake, they planned to surround and squeeze the Confederacy.

Committee of Thirteen

sine qua non

while doing little else to address the issues tearing the country apart.

the Republicans were hardly unified around a single candidate themselves

The nation’s oldest party had split over differences in policy toward slavery.

The American Civil War, the bloodiest in the nation’s history, resulted in approximately 750,000 deaths.1 The war touched the life of nearly every American as military mobilization reached levels never seen before or sinc

Trump's embrace of racism, anti-Mexican immigrant bigotry and Islamophobia is largely opportunistic. My only hesitation in calling it cynical is that I think Trump may be the type who, once he finds something convenient to say, then starts to believe it.

As mentioned above category theory has branched out into certain areas of scienceas well. Baez and Dolan have shown its value in making sense of quantum physics, itis well established in computer science, and it has found proponents in several otherfields as well. But to my mind, we are the very beginning of its venture into scientificmethodology. Category theory was invented as a bridge and it will continue to serve inthat role.

All this time, however, category theory was consistently seen by much of the mathe-matical community as ridiculously abstract. But in the 21st century it has finally cometo find healthy respect within the larger community of pure mathematics. It is the lan-guage of choice for graduate-level algebra and topology courses, and in my opinion willcontinue to establish itself as the basic framework in which mathematics is done

In 1980 Joachim Lambek showed that the types and programs used in computerscience form a specific kind of category. This provided a new semantics for talking aboutprograms, allowing people to investigate how programs combine and compose to createother programs, without caring about the specifics of implementation. Eugenio Moggibrought the category theoretic notion of monads into computer science to encapsulateideas that up to that point were considered outside the realm of such theory.

Bill Lawvere saw category theory as a new foundation for all mathematical thought.Mathematicians had been searching for foundations in the 19th century and were reason-ably satisfied with set theory asthe foundation. But Lawvere showed that the categoryof sets is simply a category with certain nice properties, not necessarily the center ofthe mathematical universe. He explained how whole algebraic theories can be viewedas examples of a single system. He and others went on to show that higher order logicwas beautifully captured in the setting of category theory (more specifically toposes).It is here also that Grothendieck and his school worked out major results in algebraicgeometry.

The paradigm shift brought on by Einstein’s theory of relativity brought on the real-ization that there is no single perspective from which to view the world. There is nobackground framework that we need to find; there are infinitely many different frame-works and perspectives, and the real power lies in being able to translate between them.It is in this historical context that category theory got its start.

The first and most ominous sign of a coming sectional storm occurred over debates surrounding the admission of the State of Missouri in 1821.

Abraham Lincoln won the 1860 contest on November 6, gaining just 40% of the popular vote and not a single southern vote in the Electoral College.

It was Kansas that at last proved to many northerners that the sectional crisis would not go away unless slavery also went away.

“Bleeding Kansas” was the first place to demonstrate that the sectional crisis could easily, and in fact already was, exploding into a full-blown national crisis.

the anti-immigrant movement simply could not capture the nation’s attention in the ways the antislavery movement already had.

The year 1855 nearly derailed the northern antislavery coalition

In the words of Amos Adams Lawrence, “We went to bed one night old-fashioned, conservative, compromise Union Whigs & woke up stark mad Abolitionists.”13

Ordinary Americans in the North increasingly resisted what they believed to be a pro-slavery federal government on their own terms.

One measure of the popularity of antislavery ideas came in 1852 when Harriet Beecher Stowe published her bestselling antislavery novel, Uncle Tom’s Cabin.

The 1852 Presidential election gave the Whigs their most stunning defeat and effectively ended their existence as a national political party.

The Fugitive Slave Act created the foundation for a massive expansion of federal power, including an alarming increase in the nation’s policing powers

By 1850, California wanted admission as a free state.

a women’s rights movement also got underway in July at Seneca Falls, New York

Left unrepresented, antislavery Free Soil leaders swung into action.

Douglass grew up, like many enslaved people, barely having known his own mother or date of birth

But the Liberty Party also shunned women’s participation in the movement, and distanced themselves from visions of true racial egalitarianism.

whites never intended them to be citizens of the United States

Even seemingly simple and straightforward phrases like “All Men Are Created Equal” were hotly contested all over again

laws tried to keep blacks out of the West entirely.

Kentucky and Tennessee emerged as slave states, while free states Ohio, Indiana (1816) and Illinois (1818) gained admission along the river’s northern banks.

Thomas Jefferson, believed that slavery was a temporary institution and would soon die ou

Vermont coming into the Union as a free state, and Kentucky coming in as a slave state

communities that would continually reignite the antislavery struggle.

English political theorists, in particular, began to re-think natural law justifications for slavery.

They generated tremendous wealth for the British crown

Southerners feared that without slavery’s expansion, the abolitionist faction would come to dominate national politics and an increasingly dense population of slaves would lead to bloody insurrection and race war.

Slavery’s history stretched back to antiquity. Prior to the American Revolution, nearly everyone in the world accepted it as a natural part of life.

Congress reached a “compromise” on Missouri’s admission, largely through the work of Kentuckian Henry Clay

Revolutionaries in the United States declared

I cannot but laugh

Do not put such unlimited power into the hands of the husbands.

"I long to hear that you have declared an independency

former slaves fled with the British army.

Americans began to create their own manufactures, no longer content to rely on those in Britain

Americans celebrated their victory, but it came at great cost

By 1781, the British were also fighting France, Spain, and Holland.

he developed his own logic of warfare

The Congress approved the document on July 4, 1776

dangerous and ill-designing men

Congress was in the strange position of attempting reconciliation while publicly raising an army.

The Congress struck a compromise

the Coercive Acts fostered the sense of shared identity created over the previous decade

Because women were often making decisions regarding which household items to purchase, their participation in consumer boycotts held particular weight

By buying the tea, even though it was cheaper, colonists would be paying the duty and thereby implicitly acknowledging Parliament’s right to tax them.

. A new sense of shared grievances began to join the colonists in a shared American political identity.

bloodthirsty British soldiers with grins on their faces firing into a peaceful crowd.

When a small number of soldiers came to the sentry’s aid, the crowd grew increasingly hostile until the soldiers fired.

colonists, once again, resisted.

In New York City, the inhabitants raised a huge lead statue of King George III in honor of the Stamp Act’s repeal.

However, the colonists rejected the notion of virtual representation, with one pamphleteer calling it a “monstrous idea

This led, in part, to broader, more popular resistance.

Stamp Act

The King forbade settlement west of the Appalachian Mountains in an attempt to limit costly wars with Native Americans.

Britain now controlled the North American continent east of the Mississippi River, including French Canada.

Both Locke and Whitefield had empowered individuals to question authority and to take their lives into their own hands.

Education would produce rational human beings capable of thinking for themselves and questioning authority rather than tacitly accepting tradition.

Perhaps no single philosopher had a greater impact on colonial thinking than John Locke

Colonial political culture in the colonies also developed differently than that of the mother country

Samuel Adams, in the Boston Gazette, described the colonies as each being a “separate body politic” from Britain.

Constant war was politically consuming and economically expensive.

But the Revolution was as paradoxical as it was unpredictable

Throughout the eighteenth century, colonists had developed significant emotional ties with both the British monarchy and the British constitution

I am not of opinion that in giving Land to the English, we deprive ourselves of the use of it, on the Contrary, I think we shall share it with them,

Neither will the Generous Inflict a Punishment without a Crime.

eternal marks traced

No group—European or Indian—held sovereign power, and diplomatic, military, trading, and social exchanges continued for much of the eighteenth century.

Native Americans living in interior regions maintained greater control over their lands and culture

the lower People,

Loudon complained about the colonists in letters to the Duke of Cumberland:

Oh that I would be a Dog or a toad or any Creature but Man

and put me into a trembling fear before he began to preach;

I saw no man at work in his field, but all seemed to be gone.

4000 of people

every horse seemed to go with all his might to carry his rider to hear news from heaven for the saving of Souls;

I dropt my tool and I had in my hand an ran home to my wife telling her to make ready quickly to go and hear Mr. Whitefield preach at Middletown

and great numbers were converted to Christ;

It is true governments cannot be supported without great charge, and it is fit every one who enjoys his share of the protection should pay out of his estate his proportion for the maintenance of it

men unite into societies that they may have the united strength of the whole society to secure and defend their properties,

The rules that they make for, other men's actions must, as well as their own and other men's actions, be conformable to the law of Nature — i.e., to the will of God, of which that is a declaration, and the fundamental law of Nature being the preservation of mankind, no human sanction can be good or valid against it.

it being ridiculous to imagine one can be tied ultimately to obey any power in the society which is not the supreme.

This legislative is not only the supreme power of the commonwealth, but sacred and unalterable in the hands where the community have once placed it

if anybody dislike, I consent with him to change it for a better.

hereditary monarchy

whoever has the legislative or supreme power of any commonwealth, is bound to govern by established standing laws

of doing whatsoever he thought fit for the preservation of himself

Secondly, in the state of Nature there wants a known and indifferent judge, with authority to determine all differences according to the established law.

he be absolute lord of his own person and possessions

'Many of the most mutinous leapt overboard and drown'd themselves in the ocean with such resolution, shewing no manner of concern for life.'

seven hundred

where he was freed.

The shrieks of the women, and the groans of the dying, rendered the whole a scene of horror almost inconceivable.

The stench of the hold

he feared that he was about to be eaten by the European crew

transatlantic slave trade

When people watch Ben’s story in the lab—and they both maintain attention to the story and release oxytocin—nearly all of these individuals donate a portion of their earnings from the experiment. They do this even though they don’t have to. This is surprising since this payment is to compensate them for an hour of their time and two needle sticks in their arms to obtain blood from which we measure chemical changes that come from their brains. 

Quakers were the first group to turn against slavery

Carolina slaves had less direct oversight than those in the Chesapeake

to avoid the diseases of the rice fields

Slave owners could not be convicted of murder for killing a slave;

This distribution of property, which kept wealth and property consolidated, guaranteed that the great planters would dominate social and economic life in the Chesapeake.

Slavery was a transatlantic institution

anti-Catholic and anti-immigrant sentiment, slowed European immigration

Jewish immigrants found work in retail, commerce, and artisanal occupations such as tailoring.

hain migration allowed Irish men to send portions of their wages home, which would then be used to either support their families in Ireland or to purchase tickets for relatives to come to the United States

Middle-class owners and managers justified their economic privilege as the natural product of superior character traits, including their wide decision-making and hard work.

Americans embarked upon their industrial revolution

enable the ‘rich’ to ‘take care of themselves’ while the poor must work or starve.

They no longer shared the bonds of their trade but were subsumed under a new class-based relationships

twenty-one-year-old British immigrant Samuel Slater to build a yarn-spinning machine and then a carding machine

cotton

steamboats filled the waters of the Mississippi and Ohio rivers

improved road networks

Her trip was less than 500 miles but took six full weeks to complete

exorbitant internal transportation costs hindered substantial economic development

America’s exports rose in value from $20.2 million in 1790 to $108.3 million by 1807

The revolution reverberated across the country. More and more farmers grew crops for profit, not self-sufficiency.

Irish, German, and Jewish immigrants sought new lives and economic opportunities. By the Civil War,

United States ended its legal participation in the global slave trade in 1808

American farmers increasingly exported foodstuffs to Europe as the French Revolutionary Wars devastated the continent between 1793 and 1815

larger exchange network connected by improved transportations

You need not be afraid to give us our rights for fear we will take too much—for we won’t take more than our pint’ll hold.

Since no written transcript of the speech has appeared,

Women’s Rights Convention

That man over there says women need to be helped into carriages, and lifted over ditches, and to have the best place everywhere. Nobody ever helps me into carriages, or over mud-puddles, or gives me any best place! And arn’t I a woman? Look at me! Look at my arm! I have ploughed, and planted , and gathered into barns, and no man could head me! And arn’t I woman? I could work as much and eat as much as a man—when I could get it—and bear the lash as well! And arn’t I a woman? I have borne thirteen children, and seen them most all sold off to slavery, and when I cried out with my mother’s grief, none but Jesus heard me! And aren’t I a woman?

He has denied her the facilities for obtaining a thorough education, all colleges being closed against her.

right themselves by abolishing the forms to which they were accustomed.

all men and women are created equal;

During the first day the meeting will be exclusively for women, who are earnestly invited to attend.

When, in the course of human events, it becomes necessary for one portion of the family of man to assume among the people of the earth a position different from that which they have hitherto occupied, but one to which the laws of nature and of nature's God entitle them, a decent respect to the opinions of mankind requires that they should declare the causes that impel them to such a course.

Missionaries worked to translate the Bible into Iroquois and other languages

word of God

an empire of benevolence

“fallen women.”

impassioned forms of worship

Women, too, exhorted, in a striking break with common practice.

Middle-class women, in particular, were able to play a leading role in reform activity.

After religious disestablishment

They began to see that they would need to fight for women’s rights simply in order to be able to fight for the rights of slave

several female reformers worked tirelessly to increase women’s access to educatio

men gained legal control over their wives’ property

Women and men of all colors were encouraged to associate together in these spaces to combat what they termed “color phobia.”

Temperance reformers pledged not to touch the bottle

After religious disestablishment, citizens of the United States faced a dilemma: how to cultivate a moral and virtuous public without aid from state-sponsored religion. Most Americans agreed that a good and moral citizenry was essential for the national project to succeed, but many shared the perception that society’s moral foundation was weakening.

Transcendentalists

As the borders of the United States expanded during the nineteenth century and as new demographic changes altered urban landscapes, revivalism also offered worshippers a source of social and religious structure to help cope with change.

Communion,

policies of their owners

Some owners allowed their enslaved people to roam, in order to scavenge for food, in times of drought or crop failures

Africans survived on the slave ships on diets which the European captain thought were appropriate for their survival

they created new instruments

American-born slaves grew up speaking these languages naturally

Europeans arrived, and as their trading presence became more concentrated

to the astonishment of the Negroes on the plantation, who thought I had made my escape to some other part of the country, as my father had done before

employed I was reflecting on many things that would present themselves to my imagination;

hen the white people would not let us be baptized by the church, we went down into the water together, in the sight of many who reviled us, and were baptized by the Spirit.