1. The dog has deep mathematical thoughts but can only articulate like a Dog. (ARF) This makes him sad.

  2. Raymond nailed it @1.
    P.S. Despite the unconvincing “right triangle” in the first panel, even the mathematically disinclined will probably recognize the Pythagorean theorem.
    P.P.S. The equation in the second panel is a little more obscure: it represents Einstein’s relativistic time dilation.
    P.P.P.S. Note that reaching the speed of light (v=c) would cause t’ to become infinite, and not negative, as all of those Star Trek episodes would have us believe. On the other hand, exceeding the speed of light would cause t’ to become imaginary. That’s why time travel only occurs in science fiction and other fairy tales.

  3. Kilby: “That’s why time travel only occurs in science fiction and other fairy tales.”

    I know someone whose physics Ph.D. thesis was on href=”https://en.wikipedia.org/wiki/Closed_timelike_curve”>closed timelike loops in general relativity, which if they exist and are stable, would allow time travel. There are such solutions to the general relativity equations, so I wouldn’t call such things “fairy tales.” There are arguments to think that some process causes these solutions to break down, so they may not exist in nature, but it’s not obvious that these arguments are correct, so given our current understanding of relativity, they may exist.

    In special relativity, it’s impossible to accelerate matter from below the speed of light to above the speed of light. However, if matter is already moving above the speed of light (tachyons), and it can interact with matter moving below the speed of light, it can be used the send messages backwards in time (ref). Again, there are also arguments that various processes prevent these things from happening, but there is at least theoretical foundation for time travel.

  4. In Sir PTerry’s book, “Pyramids”. a camel is the most brilliant mathematician in the Discworld, but of course, he cannot articulate his solutions to mathematical problems.

  5. @ WW – The mere existence of a mathematical solution doesn’t prove the physical existence of anything(*). Having endured one or two of Feynmann’s lectures (and enjoyed a whole year of Goodstein’s), I am more than willing to believe in the theoretical existence of tachyons. (I think it was Feynmann who developed the analogy that a positron was just an electron moving backward in time. It works mathematically, but it’s a little difficult to set it up in practice.) Even if someone is able to do either stunt with an elementary particle, it has nothing to do with the real world engineering that would be required to make it work for a human being (or even on a billiard ball).
    P.S. (*) – Einstein would still have become famous for all his other discoveries in 1905, but “Relativity” (for which he did not win the Nobel prize) would have remained the idle thoughts of a hair-brained lunatic, had it not resulted in physical proof of measurable manifestations (such as during the solar eclipse in 1919). As it was, confirmation of the validity of his entirely mathematical invention cemented his reputation as the world’s most famous genius. Real world experiments (and engineering**) came much later.
    P.P.S. (**) – For example, GPS satellites are designed with atomic clocks that would run incorrectly on the Earth’s surface. Once in orbit, the time dilation effect of the Earth’s gravitational field is reduced, so that the clocks are correctly synchronized with their Earth-bound counterparts.

  6. I now cannot remember the source, but some text on creativity and originality I was reading tried to make a distinction between discoveries / inventions that were sort of inevitable (and if counterfactually not announced by the people we now credit would have not much later been done by someone else), and on the other hand those that are not necessary, at least in their actual current form, and might have never been done, or not in the form we know them.

    There may have been a list (like quaternions vs vector spaces and n-tuple notation) but the key example I recall was the claim that Special Relativity was inevitable, and several people were in a position to formulate it if Einstein had not — his nominee was Poincaré — whereas General Relativity might have gone much longer without being discovered, and even so might have looked very different.

  7. https://theconversation.com/without-einstein-it-would-have-taken-decades-longer-to-understand-gravity-50517

    Not the source I remember, but a claim to much the same effect.

    “Although there is no doubting Einstein’s genius in formulating special relativity, it is generally accepted that had Einstein not published the theory in 1905, some other physicist would have done so shortly thereafter.”
    “General relativity was such a giant leap forward that it is arguable that had Einstein not formulated the theory, it may have remained undiscovered for a very long time”

  8. Kilby: I agree that the existence of a mathematical solution doesn’t prove the physical existence of anything. In fact, I believe I said several times in my comment that these solutions may not exist in nature. But the fact these are solutions to relativity equations makes them more serious than “fairy tales.”

    Your initial comment stated that the association of exceeding the speed of light with time travel was simply a misunderstanding of the math of relativity. Of course, I’m not going to generally defend the physics of Star Trek, but I’ve never seen a episode in which they said “Let’s put v>c in the time dilation equation, and we see that t’ becomes negative, so time travel is possible.” I mean, yes, if they said that, that would be wrong, but that’s not the basis of the argument for associating relativity with time travel.

  9. Re P.S.: Special relativity was quite well received almost immediately upon it’s publication in 1905, partially due to it’s theoretical simplicity, but also partially due to it’s consistency with several already-existing experimental results (e.g. Fizeau, Michelson-Morley). Of course, it needed further experimental tests, but it already had real-world experiments in support of it at time time of it’s publication in 1905.

    The solar eclipse of 1919 was experimental evidence for general relativity, and was only 4 years after the publication of GR.

  10. The Pythagorean Theorem only works for right triangles. That triangle is way off the mark.

  11. Brian in STL: It’s not the greatest right triangle, but I’d still say pretty good, for a dog.

  12. Newton’s Laws of Motion seem like they ought to have been inevitable, compared with Aristotle’s theory of impetus. Any player of a game that involved catching a thrown ball could see that the ball went in a parabola, not in a straight line then a sudden right angle and straight down.

    Heck, any dog that liked to play fetch could have told them that … except … well, I guess that’s what happened; the dogs all knew it but couldn’t communicate it to the humans.

  13. As far as Star Trek is concerned, I was referring to a (depressingly large) number of episodes and/or movies in which the strategy is “let’s fly real fast and it will send us to whatever time the scriptwriters need“.

  14. @Kilby:

    Note that reaching the speed of light (v=c) would cause t’ to become infinite, and not negative, as all of those Star Trek episodes would have us believe. On the other hand, exceeding the speed of light would cause t’ to become imaginary. That’s why time travel only occurs in science fiction and other fairy tales.

    As mentioned below, though, that’s Special Relativity, which turns out to be a simplification of the more accurate model in General Relativity.

    I’ve always found it seemingly anachronistic that Einstein was the person who finally settled the question of the atomic nature of matter (via his paper on Brownian motion). The way you learn science in grade school, that should have happened centuries before Einstein, but it didn’t.

  15. Kilby, I’m a student of the Star Trek canon and I’m not aware of any instance where time travel was achieved simply by achieving high velocities.

    They used a gravitational slingshot maneuver a couple of times (in TOS and Star Trek IV), but every other instance I can think of involves some sort of portal, wormhole, or device. 29th-Century timeships, the Bajoran Orb of Time, the Guardian of Forever… none of these involved “let’s fly real fast”. The gravitational slingshot is total bunk, of course, but if that’s what you’re referring to, there’s still more than just speed involved.

  16. @ Powers – Correct, it was the “slingshot” to which I was objecting: not just because it was “bunk”, but also because there’s no way to calibrate for a return journey.

  17. @Kilby: So David Goodstein taught a whole year of Freshman (or Sophomore) physics? After my time.

    Right after Feynman got his Nobel there was a cartoon posted on his office door of Snoopy atop his doghouse, looking depressed, and thinking “I would have won the Nobel too, but they couldn’t understand quantum electrodynamics in dog notation.”

    (In case you’ve forgotten: Feynman shared the Nobel that year with Schwinger and Tomizuka. All three independently developed QED but Feynman’s diagram notation was so much more powerful and easy to use that it;easily became the dominant approach for calculation.)

  18. Have you ever had a dog bark at you, and you knew the dog was asking for something, but you didn’t know for what? To its credit, the dog is trying to communicate, but finding it hard to communicate verbally.

    Oh, if dogs could only talk.

    In real life, dogs don’t know much about geometry and calculus (at least, we don’t think they do), but they do know a lot about the science of smells and scents — a field of study that humans have just scratched the surface of. Dogs know much more than we do about scents, and how they linger, and how they fade throughout the day, that they could teach us a lot about that scientific field, if only dogs could talk to us in English.

  19. When we throw a toy into the pool to be ‘rescued’, Gipsy, my ‘Pool Fool’, will seemingly calculate the distance she has to swim from three sides and invariably chooses the shortest distance before jumping in. Of course, she doesn’t calculate the shortest distance she has to swim to reach the steps (the fourth side, as we always throw it into the deep end), only the distance she has to swim to get to the toy. I never thought of it as calculus before, tho.

  20. But would what they know be at all relevant to us, as we have such a weaker sense of smell, nor do we have the vomeronasal organ?

    One of my dogs can smell – from inside the house, with one slider open only a few inches – that another has gone into the dogs’ bathroom (located across the patio and fenced in) and defecated. If I see her lift her head and sniff the air, I can guarantee you that it’s “cleanup in aisle five” time.

  21. @Mark Jackson — OT – Chicago is talking about renaming a couple of our parks. It has been suggested that there could be savings in replacement signage if Jackson Park could be reassigned to some other Jackson. Local hero Rev. Jesse Jackson seems favored, but others are in consideration. So be sure to contact Chicago Park District authorities if you would like to throw your hat into the ring.

    But more on-topic, I was replying to your story involving Nobel announcements.

    Recently I heard TV producer David Simon on a podcast discussing meeting with Philip Roth to discuss the planned HBO miniseries adaptation of “The Plot against America”. As it happens, Simon had heard news broadcasts that morning including the announcement of the Nobel Prize in Literature — not going to Roth. [This must have been 2017, when the laureate was Kazuo Ishiguro. Dylan was 2016.] Simon thought it would be best to mention it to Roth, and sort of kid about “sorry it wasn’t you”. Roth wasn’t fazed, but glad to hear it was a novelist. “At least it wan’t Peter, Paul, and Mary!”

  22. Mitch4: In recent arguments about restoring the original Native name for iconic local Lake Calhoun (named after fervent defender of slavery John C. Calhoun, back in the day), one wag suggested in a letter to the paper that we keep the name but claim it honored former professional wrestler “Haystacks” Calhoun.

    I assume claimed it honored old AMOS AND ANDY characterAlgonquin J. Calhoun wouldn’t have satisfied anyone.

  23. We have a section of our near-lakefront parkland named Harold Washington Park in honor of Chicago’s first black mayor, served 1983-1987, died in office, and lived near that park location in an integrated neighborhood. A little over a mile inland is a large old park called Washington Park.

    When the pandemic restrictions were established, and again when they were loosened, there were different rules for different parks — generally dividing by lakefront vs inland. There would be Harold Washington in one list and Washington in another. And people who wanted to know where they could ride bikes again were posting in social media and quoting from lists, and ended up writing “(George) Washington Park” sometimes, just to be clear. (Or actually, sometimes to obfuscate)

  24. Shrug: I live in King County, Washington. Originally it was named King County after William Rufus King, who was vice president for 45 days, and also a slaveowner. At some point they decided to “change” it to be named King County after Martin Luther King Jr.

  25. if it helps. B.A., Moderation was picking on everybody today. As opposed to yesterday when it was taking a break.

    I seems to be cyclical, but there’s apparently no rhyme or reason to it.

  26. In New York City, we have the George Washington Bridge — often referred to as the Washington Bridge (or “the GW”) — and the Washington Bridge, always referred to — obviously — as the Washington Bridge.

    This wasn’t the best thought-out idea.

  27. Speaking of not-well-thought-out ideas of nomenclature: When a western territory wanted to become a state, it wanted to be named “Columbia” after the its large river. That was nixed because it would cause confusion with the District of Columbia. So it was named “Washington”.

  28. @ Arthur – Oregon’s largest city was supposedly named by a coin flip. If the coin has fallen the other way, “Portland” would have been just another “Boston”.

  29. RE: Dogs’ sense of smell. Mark Trail [which I only see thru Comics Curmudgeon] has had that as the theme since last week . . . here is today’s strip:

  30. “Oregon’s largest city was supposedly named by a coin flip. If the coin has fallen the other way, “Portland” would have been just another “Boston”.”

    If you’re going to decide a city’s name based on a coin flip, shouldn’t the name choices be restricted to “Heads, Oregon” or “Tails, Oregon”? I mean, fair is fair!

  31. P.S. re: “the “slingshot” … was “bunk”… no way to calibrate for a return journey.
    Just now, zapping through channels on German TV, I happened to catch the relevant scene in “Star Trek IV”: Spock didn’t “calibrate” the return journey, he “estimated” or “guessed” the correct path.

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