"Let me be honest with you. If they would have asked me, 'Cam, we're going to give the team to Mac, you're going to be second string; we expect you to be everything and some to guide him throughout this tenure,' I would have said, 'Absolutely,'" Newton said. "But listen, the truth of the matter is this: He would have been uncomfortable."
On the apology, Hamilton said: "I don't know what was said beyond, that's something to ask Checo, but I think this is not something that you just apologise [for] and it's all OK. I think there needs to be more done.
This Comes As Absolutely No Surprise To Me, He Said
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The teacher giving the surprise exam "knows that his prediction is sound. But the prediction cannot be used to support a chain of arguments that results eventually in discrediting the prediction itself. It is this roundabout self-reference that [...] tosses the monkey wrench into all attempts to prove the prediction unsound."
So, the paradox of your question comes when you say, "Mathematically it looks like it should be, but that would imply that surprise exams are not possible (and they are)." Surprise exams of the first type are not possible. Surprise exams of the second type are. When you clarify the definitions, there is no paradox.
However, one thing which has always bothered me, is that in most formalizations, the surprise exam can take place in the last day, as legitimately as in any other day. To my mind, this doesn't convey the intuitive meaning of "surprise".
A new approach, given by Ran Raz here, doesn't suffer from this fallacy. He follows the "standard" logic formalization - in which "surprise" means "the exact day cannot be proved in advance (using the statement), from the fact it hasn't occured yet", but adds the clause "or it can be proved that it falls on different days" (since, obviously, if opposing facts can be proved, it is hard to say that the students "know" anything). Now, the interesting thing is, that the exam can't occur on the last day, but the induction argument fails from the unprovability of the consistency of the logical system (a.k.a. "Godel's Second Incompleteness Theorem").
The student cannot know if there will be a test even if the teacher told him so. So it's still a surprise if it happens on the very last day. And since the teacher said it will be a surprise the student wouldn't even consider it to happen on that day.
I believe that a complete explanation should delineate the exact senses in which this is surprising and in which we know certain propositions. Once this is done, then there will be nothing left to explain. One particular difficulty is that because surprise is used in an incoherent manner, we'll need a contradictory definition of surprise ("D-surprise") in order to model and explain the contradiction.
We can generate all days that would be validate exam dates by applying algorithm X as follows: First the teacher eliminates a day from the set if the student would be A-surprised. Then the teacher looks at the new set of days and sees if the student would be A-surprised on any day in the new set, repeating until no points are eliminated. It can be seen that this process will terminate and that the set produced will be precisely those that D-surprise the student.
One final point. Suppose we tell a student that they will be A-surprised. Then they will 100% know that it is not Friday. If the test happens on a Thursday, then they will experience B-knowing. This will be the last possible day, so we can see that this is actually "pretty close" to A-knowing, even though it doesn't meet the definition.
I agree that all depends on the definition of "surprise exam". If exam isn't a surprise, there is nothing saying that the exam won't be given. So the student should/could conclude (but this isn't necessarily the right thing to do) that the exam won't be a surprise instead.
I think this is a hidden-information problem. The problem is that there is no algorithm for setting the date of the exam (which can include probabilistic choices), which the student can know, which doesn't lead to no surprise in some timelines.
For example, let's say the lecturer decides "there is a 50/50 chance the exam is on the 3rd or 4th day". If the student doesn't know this, they will be surprised when the exam arrives. However, if the student does know this, then there is a 50/50 chance they will not be surprised on the 4th day.
"So if then somebody applies who doesn't fit that profile, it's likely that that person gets filtered out just because the algorithm learned from historical data," said Wachter. "That happens in recruitment, and that happens in basically everywhere where we use historical data and this data is biased."
"There's been a lot of discussion in the field about trying to come up with standards and testing periods before we deploy those systems," Wachter said. "If you have a very easy to understand algorithm detecting bias will be easier but when it comes to machine learning, a very opaque system, testing for bias and discrimination, or even understanding what's going on in that system, will become more and more difficult."
"If you look at it from the other perspective, if we play this right and if we work on data providence [...] I actually think algorithms could be a better decision-making tool than humans," she said. "An algorithm cannot lie to you, you cannot force an algorithm, you cannot entice or bribe an algorithm."
On Saturday morning, Hamas launched a major and unexpected attack against Israel from the Gaza Strip by land, air, and sea. The assault comes just after the 50th anniversary of the Israeli military being taken by surprise in the Yom Kippur War.
So Acts 18 and 19 are loaded with surprises of divine connections and friendships that were totally unanticipated. Think about it: God surprisingly brought an apostolic team of three together, and then God gave Paul a surprising connection with a pagan who so befriended him that he was instrumental in helping Paul in a difficult moment. My friend, if God can bring a team together for Paul and use an unbeliever to help Paul in a hard moment, God can do this for you too. Are you believing Him for surprising divine connections and friendships that can make a big difference in some area of your life this year? It can happen to you in 2023!
US Secretary of State Antony Blinken made a surprise visit to Baghdad on Sunday following a trip to the occupied West Bank earlier in the day. Iraqi Prime Minister Mohamed Shia al-Sudani met Blinken, the premier's office said, with the two expected to discuss the risks of escalation in Israel's war with Hamas.
It is for this reason that UVA Licensing & Ventures Group Executive Director Richard W. Chylla said Breton was chosen as the recipient of the 2022 Edlich-Henderson Innovator of the Year award. The endowed award recognizes University faculty members or a team of faculty researchers whose work is making a major impact on society.
"There is no question that there will be a challenge to the coming administration in the arena of infectious diseases," Fauci said during his "Pandemic Preparedness in the Next Administration" speech, which came shortly before Trump's inauguration on Jan. 20. He added, "the thing we're extraordinarily confident about is that we're going to see this in the next few years."
Presented in an engaging, reader-friendly style, his conclusions will surprise readers and stretch their thinking about this important subject. Heaven will inspire readers to long for heaven while they're living on earth.
There are a couple of useful verbs with this meaning too. If something unexpected, for example a piece of news or a question, throws you, it makes you very surprised and confused. Even stronger is the verb floor. If something unexpected floors you, it makes you so surprised and confused, you are unable to carry on:
"I would say that the Presidency is probably the most taxing job, as far as tiring of the mind and spirit; but it also has, as I have said before, its inspirations which tend to counteract each other . . . There have been times in war where I thought nothing could be quite as wearing and tearing as that with lives directly involved. But I would say, on the whole, this is the most wearing, although not necessarily, as I say, the most tiring."
The President's News Conference at Key West, Florida, 1/8/56
"When we get to the point, as we one day will, that both sides know that in any outbreak of general hostilities, regardless of the element of surprise, destruction will be both reciprocal and complete, possibly we will have sense enough to meet at the conference table with the understanding that the era of armaments has ended and the human race must conform its actions to this truth or die."
Letter, DDE to Richard L. Simon, Simon and Schuster, Inc., 4/4/56 [DDE's Papers as President, DDE Diaries Series, Box 14, April 1956 Miscellaneous (5)]
"The hope of the world is that wisdom can arrest conflict between brothers. I believe that war is the deadly harvest of arrogant and unreasoning minds. And I find grounds for this belief in the wisdom literature of Proverbs. It says in effect this: Panic strikes like a storm and calamity comes like a whirlwind to those who hate knowledge and ignore their God."
Address at the Centennial Celebration Banquet of the National Education Association, 4/4/57 [AUDIO]
Farley said the company is "totally committed" to a single U.S. charging protocol that includes the Tesla plug port, known as NACS. It's unclear if Ford's next-gen EVs will maintain the charging ports featured on current models, known as CCS. A Ford spokesman said the company has "this option available to us but have no news to share today."
"I thought I was dead! I thought he was dead," McDiarmid told Digital Spy. "Because when we did Return of the Jedi, and I was thrown down that shoot to Galactic Hell, [he was dead]. And I said, 'Oh, does he come back?' And [George] said, 'No, he's dead.' [Laughs] So I just accepted that. But then, of course, I didn't know I was going to be doing the prequels, so in a sense he wasn't dead, because we went back to revisit him when he was a young man. But I was totally surprised by this." be457b7860
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