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Reflection after the session:  Each participant please share your comments here before you go!

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Reflection after the session:  Each participant please share your comments here before you go!

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Share one takeaway

Ideas regards creating “ToK” / “Talk” classes

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Task: a) link to one or more IA prompts b) link to a theme or core knowledge, c) explain why and how you think it is connected to the prompt, d) link to one or more concepts

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Task: a) link to one or more IA prompts b) link to a theme or core knowledge, c) explain why and how you think it is connected to the prompt, d) link to one or more concepts

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Object 5 : Everything we see is an opinion not a fact, evaluate

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Ankhon Dekhi - Official Theatrical Trailer

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Object 3: MeowTalk: Alexa developer's app to translate cat's miaow - BBC News

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An app that aims to translate your cat's miaow has been developed by a former Amazon Alexa engineer.

MeowTalk records the sound and then attempts to identify the meaning.

The cat's owner also helps to label the translation, creating a database for the AI software to learn from.

Currently, there are only 13 phrases in the app's vocabulary including: "Feed me!", "I'm angry!" and "Leave me alone!"

Research suggests that, unlike their human servants, cats do not share a language.

Each cat's miaow is unique and tailored to its owner, with some more vocal than others.

So, instead of a generic database for cat sounds, the app's translation differs with each individual profile.

By recording and labelling sounds, the artificial intelligence and machine-learning software can better understand each individual cat's voice - the more it's used, the more accurate it can become.

The eventual aim is to develop a smart-collar, Javier Sanchez, group technical program manager at app developer Akvelon, said in a webinar on its website.

The technology would then translate your cat's miaow instantly, and a human voice would speak through the collar.

"I think this is especially important now because, with all the social distancing that's happening, you have people that are confined at home with ... a significant other - this feline," Mr Sanchez added.

"This will enable them to communicate with their cat, or at least understand their cat's intent, and build a very important connection."

The app is available free on both Google Play Store and Apple's App Store.

As it's still in its early stages of development, there are mixed reviews, with several users complaining of errors in the app.

"I'm getting quite irritated," one review said. "I just downloaded it and haven't even been able to use it because it just keeps telling me there is a wifi/connection error."

"I was getting the translation 'I'm in love!' 90% of the time," another user said.

"While it's nice to think that my cats love me so much, I'd caught one of my cats hissing and growling during play - and it said she was in love then too."

But others were positive, and the app has an average rating of 4.3 on the Google Play Store.

"For now, if you don't take it too seriously, it's a really fun app," one review said. "And, who knows, maybe in time, it will really learn my cat's true meow in all instances. It surely looks promising."

"Really cool concept and I've enjoyed it as my cats never stop talking," another review added.

However, users have also expressed concern about privacy on the app over how the data from the recordings is stored and used.

In its privacy policy, the app says it is in a "development phase" and advises anyone "concerned about data retention" to uninstall the app until it is fully compliant with the EU's GDPR privacy law

"Most cat vocalisations are actually to communicate with humans, as most owners will respond to them," Juliette Jones, cat behaviour specialist at Wood Green, The Animals Charity, said.

As the app relies on the owner labelling translations, there is room for miscommunication, she added.

"There may be some inaccuracies which could give owners the wrong impression about what their cats are feeling.

"This could be detrimental to the cat, the owner and their relationship - for instance, if a cat is purring it doesn't necessarily mean they are happy and restful. A purr can also be seeking affection or indicating discomfort. In its current form, the app should only be used for entertainment."

"We will probably never be able to convert a cat's miaow into human words," Anita Kelsey, cat behaviourist and author of 'Let's Talk About Cats', said. "All we can do is have fun thinking about what they might be saying from our own human perspective.

"The app seems like fun and there's no harm in having fun with your cat."

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MeowTalk: Alexa developer's app to translate cat's miaow

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An app that aims to translate your cat's miaow has been developed by a former Amazon Alexa engineer. MeowTalk records the sound and then attempts to identify the meaning. The cat's owner also helps to label the translation, creating a database for the AI software to learn from.

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Task: Identify the key concepts, link to any IA prompts and to a theme,  explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme,  explain why and how you think it is connected to the prompt.

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Object 4:

How Social Media Shapes Our Identity- The Internet constantly confronts us with evidence of our past. Are we losing the chance to remake ourselves?

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Last year, I had a strange dream. My father and I were wading in an industrial canal, reminiscent of a subway, as thousands of hatchery-raised fish were being released into it. The fish crowded, slimy, around our legs, and I knew (in the way that one knows in a dream) that they thought, as they hit the water, that they were drowning-that they had to experience death before entering adulthood. The next day, I told my father about the dream. He revealed that, when I was three, when we were living in Pittsburgh, he took me to see a truckful of catfish being pumped into an artificial pond. I was too young to remember this. But somewhere in my mind the vision of fish being spewed into water had lodged itself, resurfacing more than twenty-five years later.

These days, it's common to find an image emerging, unbeckoned, from the reservoir of the past. We spend hours wading through streams of photos, many of which document, in unprecedented ways, our daily lives. Facebook was invented in 2004. By 2015, Kate Eichhorn writes in " The End of Forgetting: Growing Up with Social Media," people were sharing thirty million images an hour on Snapchat, and British parents "posted, on average, nearly two hundred photographs of their child online each year." For those who have grown up with social media-a group that includes pretty much everyone under twenty-five-childhood, an era that was fruitfully mysterious for the rest of us, is surprisingly accessible. According to Eichhorn, a media historian at the New School, this is certain to have some kind of profound effect on the development of identity. What that effect will be we're not quite sure.

Eichhorn sees both sides of the coin. On the one hand, she says, children and teen-agers have gained a level of control that they didn't have before. In the past, adults refused to acknowledge children's agency, or imposed on them an idealized notion of innocence and purity. Adults were the ones writing books, taking photos with expensive cameras, and commissioning paintings, all of which tended to commemorate childhood-to look back at it-rather than participate in it. The arrival of cheaply made instant photos, in the nineteen-sixties, allowed children to seize a means of production, and the arrival of the Internet gave them an unprecedented degree of self-determination. "If childhood was once constructed and recorded by adults and mirrored back to children (e.g., in a carefully curated family photo album or a series of home video clips), this is no longer the case," Eichhorn writes. "Today, young people create images and put them into circulation without the interference of adults."

This practice can be hugely beneficial. New technology-especially the smartphone-allows us to produce a narrative of our lives, to choose what to remember and what to contribute to our own mythos. For Eichhorn, this is the latest instance of a long-held, if mysterious, practice. "Long before children were able to create, edit, and curate images of their lives," she writes, "they were already doing so on a psychic level." Freud called these images "screen memories"-no pun intended-and he thought that we used them to soften or obscure painful experiences. Humans have always tried to cope with the difficulty of memory, to turn it "from an intolerable horror to something which is reassuringly innocuous and familiar." Social media just makes us more adept at it.

On the other hand, Eichhorn writes, such media can prevent those who wish to break with their past from doing so cleanly. We're not the only ones posting; our friends and family chronicle our lives, usually without our consent. Growing up online, Eichhorn worries, might impede our ability to edit memories, cull what needs to be culled, and move on. "The potential danger is no longer childhood's disappearance, but rather the possibility of a perpetual childhood," she writes. We may, in short, have traded "screen memories for screens."

This is of particular import for those who yearn to establish new identities. People who transition, for instance, often rely on having a clean break, visually, with their previous appearances; as Eichhorn points out, one of the early promises of the Internet, when it was just "texts and clip art," was that it "presented itself as a safe place [for transgender youth] to try on an aspect of their identities they could not explore in their material lives." Now that the Internet is more permanent, and more pervasive, it's hard to avoid the relics of past identities. Eichhorn cites one of her students, Kevin, an aspiring film critic from a small town in upstate New York. By his second year of college, Kevin says, his Facebook stream "was getting really weird. I had my new friends from New York posting about queer performance art and these guys from my high school posting about dirt biking in a gravel pit and tagging me in photographs from high school. I needed to move on." Although he deactivated his social-media accounts and created new ones under a pseudonym, he continued to be tagged in old photos. "I guess that Kevin is out there for good," he says. "I just have to live with him and all those people he was trying to escape."

The persistence of certain images is more of a problem for some than for others. There are moments, elevated not by the fact of being recorded but by the impossibility of being erased, that become traumatic. These situations-in which a naked photo or an offensive tweet destroys a person's public life-are unfortunate, and widely covered (for example, in Jon Ronson's " So You've Been Publicly Shamed "). Eichhorn details the case of Ghyslain Raza, a Canadian teen-ager who, in 2002, recorded himself wielding a golf-ball retriever as though it were a lightsabre. The video, which was found by a classmate, titled "Star Wars Kid," and uploaded to the Internet, was viewed by millions of people; as Eichhorn points out, this all happened at a time when virality, as a phenomenon, wasn't really a thing. Raza was bullied at school and ended up in a psychiatric ward. In 2013, still unable to escape the video, despite legal action, he spoke publicly about his experience, describing his contemplation of suicide.

Everyone, Eichhorn writes, benefits from experimentation in adolescence. During that time, we exist in what the psychoanalyst Erik Erikson called a psychosocial "moratorium"-a stage in which we hover "between the morality learned by the child and the ethics to be developed by the adult." The moratorium is a period of trial and error that society allows adolescents, who are permitted to take risks without fear of consequence, in hopes that doing so will clarify a "core self-a personal sense of what gives life meaning." The Internet interrupts the privacy of this era; it tends to scale up mistakes to monumental proportions, and to put them on our permanent records. Colleges and employers now look at social-media accounts for evidence of character. Eichhorn spends less time than she might have on how this affects today's teens. What is it like to live under threat? What are the ramifications when an entire generation never gets the chance to experiment freely or to remake themselves?

Eichhorn does lightly gesture to a kind of universal human right, one that runs counter to the whims of companies that use data. "Forgetting-that once taken-for-granted built-in resource that all humans possessed-is now being pitted against the interests of technology companies," she writes, implying, with an endearing idealism, that we have a right to forget. (For some, this belief might reflect a distinctly American approach to the rest of the world.) More plausibly, she cites the right to be forgotten, which is the nickname of both data privacy regulations in Europe and movements against naming minors in the media. Either way, the implication is that the ability to detach from one's past self-to move laterally, as an individual, into a new body or personality-is a democratic ideal. We also have the right to stay as we are. In some cases, retaining our sense of self across chasms that might destroy it is more important than having a rebellious phase. Take, for instance, the case of migrants, which Eichhorn touches on briefly: "Family members left behind can now stay in constant touch with their sons and daughters and even track their footsteps across Europe." Here, memory is almost a form of political representation, enabled by social media; groups are able to preserve their history as they travel across continents.

Are all photos documentary? In " The Social Photo," Nathan Jurgenson puts forth the useful proposition that most online photos are about sharing experiences, not creating memories. In one passage, Jurgenson, a founder of Real Life magazine, writes that selfies are "less an accurate picture of me at this time in this place and more . . . a visual depiction of the idea of me." They're units of communication, more emojis or hieroglyphics than portraits; they have little context, aren't discernibly located anywhere, and typically come in the aggregate. For the most part, it wouldn't really matter if they existed in twenty years. This explains the prevalence of disappearing photos, like Instagram stories and Snapchat. (Jurgenson is also a sociologist for Snap Inc., Snapchat's parent company.) It also explains photos of food, which are rarely artful or worth saving.

For Jurgenson, taking social photos changes the way vision works-a process that began with the advent of cameras and is still evolving today. Teen-agers are cyborgs, and their phones are mechanical eyes that help them interpret their experience. "To document," Jurgenson writes, "is to be involved with our own experience instead of passively letting it float by." On this subject, Jurgenson has all the right, if somewhat dutiful, opinions: nostalgia is overrated, but he's not into "digital austerity." We shouldn't hark back to an era in which we were less attached to technology-mostly because that era doesn't exist. "Our reality has always been already mediated, augmented, documented," he writes, "and there's no access to some state of unmediated purity." We shouldn't ask whether social photography is good, but how it can be good.

Jurgenson, unlike Eichhorn, isn't worried about the Internet making it hard to bury past versions of ourselves. If anything, he fears the prevalence of death. Photos, he writes, "embalm" their subjects, encasing them in a "stilling sadness that kills what it attempts to save out of a fear of losing it." For him, the risk of constant documentation is alienation: a sense that our bodies are generating still moments rather than constant movement. He cites Wolfgang Schivelbusch, a German scholar who wrote about the effect of the railway on human perception. With its speed and glass windows, "the train flattens nature into something smooth and predictable, not something traveled within but something easily seen and consumed," Jurgenson writes. "As more of life is experienced through camera screens, does it occur at a similar remove, where the messiness of lived experience is made into something merely observable?"

It would, indeed, be stunning if we were able to see painful moments from the past-the ones we meditate on for years-as dead and embalmed. The trouble is, most difficult memories aren't captured by photos, videos, or tweets. Screens, like screen memories, are avoidant; they turn away from the painful. There are few crying children on Instagram. A friend, whose mother digitized all her family's old home videos, recently told me about a significant birthday party at the roller rink. What she remembered was the drama beforehand: at the time, she was obsessed with Rollerblades, and when the rink had only roller skates her mother rushed to a sports store to get an inline pair, barely saving the day. None of this, it turned out, was captured in the video. All it showed was the triumph-a redemptive moment after tears, and a happy loop around the rink.

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Nausicaa Renner writes on how the Internet-especially social-media platforms like Facebook, Instagram, and Snapchat-makes it difficult for people to escape their previous identities.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Object 6: https://www.livescience.com/24310-flat-earth-belief.html
A Flat Earth model depicting Antarctica as an ice wall surrounding a disc-shaped Earth.(Image: © Creative Commons 1.0 Generic/Trekky0623)

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Task: Identify the key concepts, link to any IA prompts and to a theme, explain why and how you think it is connected to the prompt.

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Object 2 - 2+2=4 - How?

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This question was featured on Saturday Morning Breakfast Cereal and I haven't been able to find a proof. Can anyone help?

Asaf Karagila ♦

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When proving theorems in mathematics, one starts from a set of axioms, statements that are accepted as true without argument. You might ask, "but what if an axiom isn't true?", and the answer is that we would be dealing with different mathematics. For example, Euclid included the parallel postulate as an axiom in his elements. For years mathematicians tried to prove that the parallel postulate could be derived from the other axioms. It turns out that if you don't accept the parallel postulate, you end up with different types of geometry that we now call non-euclidean. Einsteins theory of general relativity depends on these geometries.

To come up with a proof of such a seemingly simple fact as $2 + 2 = 4$, we need a set of axioms to start with, and we need precise definitions of all the terms we are using. Depending on what set of axioms you start with, proving that $2 + 2 = 4$, and that no other natural number can equal $2+2$ may be either very simple or surprisingly difficult. For example in Russell and Whitehead's Principia, it famously took over 300 pages of work before they could prove that $1+1=2$. They started with a very sparse set of axioms though.

The most common set of axioms for the natural numbers are the Peano Axioms.

They are

1. $0$ is a natural number.

2. For every natural number $x$, $x=x$.

3. For all natural numbers $x$ and $y$, if $x = y$, then $y = x$.

4. For all natural numbers $x$, $y$, and $z$, if $x = y$ and $y = z$, then $x = z$.

5. For all $a$ and $b$, if $a$ is a natural number, and $a = b$, then $b$ is a natural number.

6. For every natural number $n$, $S(n)$ is a natural number.

7. For every natural number $n$, $S(n) = 0$ is false.

8. For all natural numbers $m$ and $n$, if $S(m) = S(n)$ then $m = n$.

9. If $K$ is a set such that $0 \in K$, and for every natural number $n$, $n \in K$ implies that $S(n) \in K$, then $K$ contains all natural numbers.

Here $S$ is the successor function, it takes each natural number to its successor. This might seem like a complicated mess compared to the simplicity of natural numbers, but we need to be precise. We need to carefully construct the axioms so that no contradiction can be derived from them, and so they encapsulate what we understand to be the natural numbers. We want to be able to prove interesting statements about the natural numbers from them. Note that the axioms contain undefined terms. The axioms don't need to state what the terms mean, only what they do.

The following definitions are commonly used within this axiomatization. They are the definitions from Peano's original paper (An English translation is available in the book From Frege to Gödel), modified to start at $0$ instead of $1$.

$1$ is defined as $S(0)$, $2$ is defined as $S(1)$, $3$ is defined as $S(2)$, and $4$ is defined as $S(3)$. Addition is defined recursively as follows.

$$a + 0 = a$$ $$a + S(b) = S(a + b)$$.

Thus

$$2 + 2 = 2 + S(1) = S(2 + 1) = S(2 + S(0)) = S(S(2 + 0)) = S(S(2)) = S(3) = 4$$

proving that $2+2 = 4$.

This is the unique value of $2+2$ by axiom 4.

If $x = 2+2$ and $2+2 = 4$, then $x = 4$.

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From the Peano axioms.

First recall that $2$ is really a shorthand for $S(S(0))$ and $4$ is a shorthand for $S(S(S(S(0))))$. Now we have the axioms for addition, $x+0=x$ and $x+S(y)=S(x+y)$. We calculate:

$$2+2=S(S(0))+S(S(0))=S(S(S(0))+S(0))=S(S(S(S(0))+0))=S(S(S(S(0)))=4$$

To prove uniqueness we use the axioms that $0\neq S(x)$, $x\neq0\rightarrow \exists y(x=S(y))$ and $S(x)=S(y)\rightarrow x=y$:

$$S(S(S(S(0))))=S(S(0))+S(S(0))=x\implies\exists y(x=S(y))\implies S(S(S(0))=y\implies\exists z(S(z)=y)\implies z=S(S(0))=2$$

Therefore $z=2$ and so $y=3$ and $x=4$ as wanted.

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The question doesn't make sense; the definition of $2 + 2$ doesn't involve an indeterminate, so there's no "solution" to be had, just the fact that $2 + 2 = 4$.

Contrast this with $\sqrt{4}$, which could be interpreted as "a solution to $x^2 = 2$", in which case there are two solutions, $2$ and $-2$.

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The cartoon is a joke which doesn't bear too much analysis. The "mathematician parent" is the cartoonist's parody of such a parent. A real mathematician would not ask for a proof that the "solution is unique" in the case of addition of two specific integers, because such a request would make little sense. If we must credit the request with some sense, then perhaps an appropriate response would be at the level of "because addition is unique, Stupid!".

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$+$ is an operation, which means it is a function. The rest follow from definition of a function.

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You need a mathematical proof by contradiction.

You assume 2 plus 2 is not equal 4.

2+2 <> 4

You substract 2 from the two sides of the equation.

2+2-2 <> 4-2

2 <> 2

2 is not equal to 2? CONTRADICTION. Thus, proof.

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Prove it geometrically...

1. Fist define your "anchor/base" unit -> a line with a defined length is #1.

2. Next define #2... just join 2 of your #1 units... and postulate it's #2, the double of the "base"... you can measure it... then you can prove it...

3. draw 2 of your #2 units, parallel in the geometric space, like in a vector space...

4. Draw the next sequence -> Move the beginning of the the 2nd #2 to the end of the 1st #2 and voilá... you have #4

*you can prove all the relations -> #1 = 1x #1 | #2 = 2x #1 | #4 = (4x #1 or 2x #2) *if at a superior academic level you have to define and prove the operations also '+' and 'x'... at least the "neutral element" of operation 'x'... Good luck...

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Prove that $4$ is the only solution to $2+2$.

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Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Sign up to join this community Asked $\begingroup$ This question already has answers here: Closed 6 years ago.