Go Forth and Multiply

123 × 321 = 39,483

My interest in number multiplication goes back to exploring algorithms for generating Mandelbrot plots, which can require billions of multiplication operations on arbitrary precision numbers (numbers with lots and lots of digits).

Multiplying two numbers — calculating their product — is computationally intense because of the intermediate Cartesian product. Multiplying two 12-digit numbers creates a 24-digit result (12+12), but it also has an intermediate stage involving 144 (12×12) single digit multiplications.

Recently I learned an intriguing Japanese visual multiplication method.

For quite some time I’ve had notes about a possible post regarding the Cartesian product aspect of multiplication. Discovering this Japanese method provided a long-sought hook for it.

As I mentioned, Mandelbrot plots can require billions of multiplications, each with hundreds, even thousands, of digits, so it’s a topic of interest to me.

The thing about multiplication is that that the number of significant digits grows with each operation. A multiplication product has as many digits as its two factors combined. Multiplying two 50-digit numbers creates a 100-digit number. So would multiplying a 20-digit number times an 80-digit number.

The Mandelbrot algorithm. Z and C are complex numbers.

The Mandelbrot formula starts with a given number, Z and squares it — that is, multiplies it by itself.

It adds another given number, C, to the product and uses the result as a new Z to keep repeating the calculation until it gets a result greater than two. (If this never happens, then C is in the Mandelbrot set.)

The thing is, each time through the loop, since Z multiplies itself, the number of digits doubles. That can’t be sustained for billions of operations, so at some (very large) length, the numbers are truncated and some precision is lost.

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Here’s the killer part: Say we truncate our numbers at 500 digits. That’s a precision level way beyond Planck level (which is a mere 34 digits). But there are Mandelbrot zooms using thousands of digits, so we’re being quite reasonable with 500-digit numbers.

The product will have 1000 digits, but generating it requires 500×500 single-digit multiplications (each of which generates a two-digit intermediate product).

That’s 250,000 intermediate multiplications — the Cartesian product of two 500-digit numbers. That’s a lot of intermediate calculations to generate a result.

Note that a Cartesian product is naturally a table of rows and columns, like a spreadsheet. Summing the table cells along diagonals generates the multiplication product. (See illustration at top.)

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The Japanese visual method for multiplication illustrates the tabular nature of the intermediate Cartesian product. The fun part is that it does it using base one arithmetic.

Figure 1.

Let’s say we want to multiply 42 × 65. We start by drawing lines as shown in Figure 1.

For the first number, use lines that slant down to the right, and draw as many lines to match each digit. Note the number, as numbers do, flows from left-to-right — first the 4 and then the 2.

For the second number, use lines that slant up to the right, and again draw as many lines for each digit. Note again the number flows left-to-right, first the 6, then the 5.

To keep things clear be sure to keep some separation between the digits, and keep your lines nice and neat.

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Figure 2.

The next step is to count the number of intersections in each group of lines crossing. In this example, there are four such groups (Figure 2).

This is the base one arithmetic part. Each line crossing counts as one, and the total count of a group turns out to be the product of multiplying those two digits.

For example, in the top group, there are 12 line intersections (in a 2×6 grouping), and obviously 2 × 6 = 12.

The other three groups are similar — each is the product of multiplying the two digits involved. All four groups comprise the intermediate Cartesian product of multiplying 42 and 64. Each group itself is a Cartesian product of multiplying two digits.

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Figure 3.

Now we sum the groups.

We do this left-to-right starting with the first corner.

Then we combine matching corners. That can get a little tricky if the two factors have a different number of digits, but when both numbers have the same count of digits, the resulting diamond shape is simple.

(In fact, this technique is beautiful and interesting, but somewhat limited to numbers with only a few digits and — ideally — the same number of digits or nearly so. As you’ll see, things get unwieldy fast, which is only to be expected with base one arithmetic.)

The result is a row of sums across the bottom (see Figure 3).

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Figure 4.

The final step is just to carry the overflows.

This time we work from right-to-left, starting with the 10 and ending with the 24.

Starting with the 10, we carry the 1 to the left and keep the 0, so the rightmost digit of the final product is a 0.

The carried 1 increases the 32 to 33. We carry the tens 3 and keep the ones 3, so the next digit of the result is 3.

The carried 3 increases the 24 to 27. We carry the 2 and keep the 7, so the third digit is 7.

The carried 2 is alone, so it’s the final digit of the result product.

And, sure enough, 42 × 65 = 2730.

§ §

It’s a cute trick in that, if you really do just count the line intersections, there is no actual multiplication involved — just counting and addition.

It would be possible, but beyond unwieldy, to treat 42 and 65 as the single numeric quantities they actually are (rather than as a pair of base ten digits).

That makes the two numbers single “digits” (“symbols” is a better term here), and we’d draw it as a single group with 42 lines crossed by 65 lines. The count of all the intersections is 2,730 — the literal Cartesian product of 42×65.

By the way, area is another Cartesian product. A 50′ by 40′ field has 2000 square feet. Think of each square foot as an intersection among the 50 by 40 lines drawn each foot.

It’s a topic I’ll return to in the future, but for now an important point is that, with regard to multiplication’s intermediate Cartesian product, “digit” can be any numeric container we need (which is why “symbol” is a better term).

As the Japanese method demonstrates using base one, multiplication is ultimately just counting a Cartesian product. I find especially interesting that it’s easy to work with any numeric base due to how carry is deferred until the final step. Input and output numbers can be in any base.

(That’s a post for another time.)

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Above I mentioned that multiplying two 50-digits numbers results in a 100-digit result.

The same goes for multiplying a 20-digit number times an 80-digit one. For that matter, likewise multiplying a one-digit number times a 99-digit number.

(Caveat: potentially; the result can be one digit shy. As a trivial example, 2×4=8, but 2×5=10. The upper limit is “all nines” numbers, 99×99=9801. In contrast, 11×11=121.)

There is a lot more difference when it comes to the intermediate products, though. Multiplying two 50-digit numbers generates a Cartesian product of 2500 values (50 rows, 50 columns). But when they are 20-digits and 80-digits, the intermediate table has only 1600 values.

And in the case of one-digit and 99-digits, there are only 99 intermediate values!

(It shows why the Mandelbrot calculation is such a killer. Squaring a number, by definition, means both factors are the same length, which is the worst-case scenario in terms of Cartesian product.)

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As you might imagine, this business of drawing lines can get unwieldy. If we’re willing to forego the counting and do single-digit multiplying, this visual method is a bit easier (if less visual).

Figure 5.

Rather than draw base one lines we must count, draw a single line for each digit (see Figure 5).

Rather than count lines intersections, at each digit crossing we do the single-digit multiplication we learned in grade school from multiplication tables.

Essentially we’re hiding counting the visual Cartesian product and using rote memory instead.

As an aside, a multiplication table is a Cartesian product generated from two matching sequences of integers. (Since the integer sequences are infinite, the table is “infinite-squared” — which is just infinite. Both are enumerable and, hence, the same size of infinity.)

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Figure 6.

Once we have the set of intermediate products (by multiplying rather than counting this time), the process proceeds as before.

We sum the diagonals starting at the leftmost corner and working across (see Figure 6).

(I’ll note again this looks more complicated when the two numbers are quite different in length, but it’s just a matter of lining up corners. As a self-check, you should always end with the rightmost corner on its own. In fact, you could work right-to-left from that rightmost corner. That would align nicely with the carry, which ripples right-to-left.)

You might notice this looks somewhat like the standard grade school technique of long multiplication.

In fact it does very much resemble it. A notable difference involves the carrying. Long multiplication does it throughout while this method defers it to the end.

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The post I have notes for involves something very similar to, even isomorphic with, the Japanese visual multiplication method (although more in the reduced form shown directly above).

The image at the top of this post illustrates a “grid” method of multiplication, and you can see the similarities if you rotate the image at the top 45° clockwise, or if you rotate the Japanese diagrams 45° counter-clockwise. Either way, it’s the same sort of thing — a Cartesian product summed diagonally.

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I may return to pick up the thread (although maybe not; perhaps this covers the topic well enough). For now, I’ll leave you with some images.

One night I got to thinking about how to code an algorithm to create images of the Japanese multiplication method.

Figure 7.

As it turned out, pretty easy (like just a couple hours messing around got most of it done — the polishing took several times as long).

It was easy to code because I rotated the images 45° counter-clockwise (which aligns them with the image at the top of the post). Note that the first number, 123, runs along the left from bottom-to-top, and the second number, 789, runs along the top from left-to-right.

The thin red lines show the summing diagonals. In the image above (Figure 7), starting with the lower-left corner, the sums are: 7, 22, 46, 42, 27.

The carry ripples from right-to-left:

  • 277, carry 2
  • 42+2=44→4, carry 4
  • 46+4=50→0, carry 5
  • 22+5=27→7, carry 2
  • 7+2=9→9

Giving us our final result: 97,047.

There are some limits to the technique:

It does get a bit crowded, especially with nines. (Although I can always just make the image larger.)

These two used factors with the same size, which results in a square grid with nice 45° diagonals (the ideal case for the Japanese method). You can easily rotate this to make it look exactly like that method.

It’s a bit less elegant when the numbers are different lengths:

The trick is to start at one corner and work across. (Or write code to do it!)

The algorithm requires each number have at least two digits, but it’ll accept leading zeros to create a minimal example:

(A true minimum would be 1×1, but that’s too boring.) Note how, when a digit is zero, there are no line intersections to count. In this case, only the upper-right corner — the last corner — has a non-zero value.

One tweak my algorithm needs is better spacing when there are only two digits. It only looks good with three or more. (And then not too many.)

Still. It makes pretty pictures, which was mainly the point.

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Until anon.

Go forth and spread beauty and light!

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

23 responses to “Go Forth and Multiply

  • Wyrd Smythe

    For those with an interest, I’ll post the Python code on my other blog. (I’ll shoot for soon. It’s been a while since I posted there, anyway. High time to get back to it.)

  • Wyrd Smythe

    Something that might distract me in the meantime: The code for drawing the lines at angles seemed a lot harder, especially matching up the diagonals, so I used a rectangular grid to simplify the calculations.

    But it occurs to me I could use a rotation matrix (or quaternion!) to transform the points to a 45° rotation. I might play around with that today…

  • Wyrd Smythe

    So, um, that idea about using a rotation matrix? Turned out to be surprisingly easy…

  • Wyrd Smythe

    Still need to fix the spacing on two-digit numbers, though…

    All the other values are fine, so I can probably get away with just special-casing it.

  • Wyrd Smythe

    This example shows the extreme angle when the two factors have different lengths:

    As mentioned in the post, the trick is starting at one corner, either the left or the right, and working across. It can get a bit eye-watering, though, which is why I spent so much time figuring out how to draw the diagonals. (It was the trickiest part of the code.)

  • Wyrd Smythe

    There’s an interesting way to look at the Mandelbrot that illustrates the weird dual nature of being able to compute (at least in theory) the compliment of the M-set, but it’s not possible to compute the M-set. (Both sets are uncountable, but only one is computable.)

    Imagine a function, M, that does the Mandelbrot computation:

    M ≜ function(z): z2+c

    For any given z, it does the calculation and returns the result (which is plugged back into the next iteration as the new value of z). What’s missing so far is a value for c.

    So imagine a function that returns a function that does the computation:

    M ≜ function(c): function(z): z2+c

    The value of c is the particular coordinate we’re calculating. We can imagine a parallel system where each thread calls M with a different c to calculate pixels in parallel.

    The point is that normally we’d use M to create a function, let’s call it g, which we’d call repeatedly. We’d start with 0.0 (or the value of c, since that’s always the second iteration’s result). We’d keep passing the result back into g until we get tired or the result “escapes.”

    But another way to think of it is recursively:

    g = M(0.26)
    z = g(g(g(g(g(…g(g(g(0.0)))…)))))

    Where the number of recursions is the max interations. (Computationally hugely wasteful, if not effectively impossible, but we’re talking theory here.)

    Either the final result, z, will be above the max or not. If it’s above, the point, c, is outside the M-set. If it’s below, the point is undetermined (further computation may case the point to escape).

    So in some sense, for a given level of iteration, the M-set compliment is determined on a calculation that doesn’t require a computation. That is, the expression “(z*z)+c” can be directly calculated (in principle) and therefore any specific number of recursions can also be directly calculated.

    For example, three levels is: ((((((c*c)+c)*((c*c)+c))+c)*((((c*c)+c)*((c*c)+c))+c))+c)

    If you unwind is the same as: g(g(g(c)))

    (There’s no point in starting at 0.0 because the value of (0*0)+c is always c, so might as well just start there.)

  • SelfAwarePatterns

    I’ve got nothing on the mathiness. But wondering how your reading of The Expanse is going, and what you thought of it.

    • Wyrd Smythe

      But the mathiness is so much fun! 😀

      I’ve read all eight books now. I still like 4 & 5 the least, but 6 involves the unraveling of Marcos Inaros, so that was okay. And 8 likewise involves the unraveling of Laconia, so that was okay, too. The gang is back together (albeit with a sacrificed pawn), so it’s looking set for the final book.

      And Amos is fixed now. 😮

      I’m not sure what to think of the Big Threat. Kinda almost makes this a monster story with strong Frankenstein overtones. Rather than an alien contact story or a solving technology issues story. The first trilogy,… it could have gone either of those directions. But it didn’t. [shrug]

      (I’ve thought about a followup post. But haven’t gotten around to it. I’m dog-sitting Bentley this weekend, so it won’t be this Sci-Fi Saturday, that’s for sure.)

      • SelfAwarePatterns

        Wish the mathiness was fun for me. I can only find it interesting when it’s directly tied to figuring out something about the world.

        Yeah, I was mildly surprised things ended moderately happy at the end of 8. Makes me wonder what awful thing is coming in 9. I’m hoping it involves our heroes journeying into the otherspace or whatever where the aliens are.

        I thought the Amos development was interesting. They made a point of showing that the girl was still sentient so we’d be primed to accept him that way. It might be the closest the series will get toward any kind of posthumanism. (Well, other than the gory example of the dictator.)

        I also thought you’d like the implication that consciousness is a quantum phenomenon that can be targeted by a weapon.

      • Wyrd Smythe

        It’s one of those things I don’t quite grasp about others. To me, math is foundation knowledge that underpins everything, so how could it not be fascinating? 😀 I think part of it for me is that I find the Platonic/Nominalist question as intriguing as other major questions, such as the nature of time (and space) or the nature of consciousness (or abiogenesis or the Big Bang and the very nature of existence) — all fascinating to me. But then I’ve long self-identified as a philosopher.

        [Huh! There’s a post I never got around to writing, although it should have been one of my earlier ones. A simple question (that one should spend time thinking about about before answering): Pick three key words that identify oneself. Sum up who one is in three carefully considered words. Mine, for a long time, were “artist,” “teacher,” & “philosopher.” I haven’t thought about it in ages! They still resonate, but I’ll have to think about it a bit.]

        Destruction of entire worlds aside, The Expanse, as I’ve mentioned, is actually fairly joyful — which is only proper for space opera, which usually has a bit of ‘Earthman über alles’ flavor. Humans are ever and always just… better. Kirk said it often — it was often an underlying theme to his big speech.

        “I also thought you’d like the implication that consciousness is a quantum phenomenon that can be targeted by a weapon.”

        There was a line that cracked me up. I knew you’d think I’d notice it. 😉

        I know some disdain the idea that two unanswered questions, self-awareness and the nature of quantum reality, might be connected — the pushback against the idea of linking them just because they’re both mysteries. But what if they are, in fact, connected?

        (I know the canonical answer about no evidence for it. But there was no evidence for a lot of discoveries until there was. When I was a field tech, clients would sometimes complain, “It was working yesterday,” — similar to, “He was alive just yesterday,” — and I’ve never understood the logic. The light bulb was just fine,… until it burned out. Lack of evidence, as the old saying goes, is not evidence of lack. It’s, at best, suggestive, but not meaningful.)

        But I digress. The Expanse, to a large extent, is very much the sort of SF I really enjoy. I burned through books 7 and 8 pretty quickly. I think I was put off by a perceived “frontier Western” nature of book 4 (never really loved colonization SF) and then seriously put off by book 5. The helplessness of the Solar System against Laconia in book 6 was tough, but I could already see the cracks in that empire, so books 7 and 8 tended to follow my expectations. The arc for Duarte was obviously the Prometheus hubris arc. I enjoyed watching it play out.

        Bottom line, I’d read the whole series again some day (if I had time — point is, I’d be willing to read it again).

        The question of Amos does touch on the zombie question. Amos (and the two kids) self-reported that they were conscious, and that report seemed rich and vivid, so wherein would be any reason to doubt consciousness?

        Also touches on the discussion about animal behavior being tied to their consciousness. Dog, I think, have a form of self-reporting, and so do the higher primates. I wonder about elephants, crows, octopuses, and cetacean, too.

        What’s interesting about Amos involves who he was — and what might have been missing from him already — compared to who he is now. Would Holden (funny how it’s Alex, Naomi, and Amos, but it’s always Holden, never James or Jim) transition as thoroughly? It would be interesting to explore.

      • SelfAwarePatterns

        Maybe if I’d been bit by the platonic bug, I’d find math more interesting. But for me, it’s always just been a tool. I find it a cool tool when it reveals something about reality, but in and of itself, I just can’t garner enthusiasm for it. My math grades in school always showed it too.

        Someone recently told me they thought my interest in computer programming likely came because I could see the practical uses for it, while for math it was always a distant promise. I think there’s something to that. For me, teaching math as a subject totally divorced from what you can do with it made the whole subject a chore. I always felt the enthusiasm of my math instructors for their subject matter, but to me is was like being enthusiastic over wrenches and hammers.

        My biggest issue with quantum consciousness is it seems like part of a long list of things people want to be true, so they cherry pick for evidence for it. But if you read a neuroscience textbook, the only place you might see the word “quantum” is for some of the scanning technologies. (The same for electromagnetic fields.) There’s just nothing in the current data really motivating it.

        The Expanse authors once noted that each book in the series is actually exploration of some particular genre. So 4 probably was their frontier one. I don’t know what 5 was, except maybe just a disaster story. That said, that was several years ago, so I don’t know if that’s what they’re still doing.

        Amos was an interesting character for that to happen to. He’s pretty much a psycho, but one who realizes he is and grounds his ethics in what others would think. Like you said, it probably was an easier transition for him than for others.

        I’m a little bit leery of labeling what a lot of animals do as report. I know cognitive scientists do it, and it might be somewhat plausible for some species, such as primates. But the further down in intelligence we go, it seems like the stronger our interpretation of the behavior has to be to see it as report (in the sense of communication) rather than just an operantly learned action.

      • Wyrd Smythe

        “My math grades in school always showed it too.”

        Whereas they put me in advanced classes in high school, so, yeah, I guess it’s just one of those things you take to or not (like most things in life). Once I got deeper into the arts, math kinda fell by the wayside for a long time, although computer programming brought it back. But it’s only been in the last decade or so I’ve gotten really interested in the philosophy and foundation of it all.

        “Someone recently told me they thought my interest in computer programming likely came because I could see the practical uses for it,”

        I think that does speak to a basic difference between us. I’m much more into the abstractions. (Yet, ironically, I’m more of an absolutist. Go figure.)

        I do think the early teaching is crucial. Teaching math as a rote skill really kills the attraction. History is similar. It can be rote memorization, or a teacher can really bring history to life. Likewise, some math teachers can do the same with math.

        “My biggest issue with quantum consciousness is it seems like part of a long list of things people want to be true,”

        Yeah, maybe so, but that’s a social observation not particularly related to analysis of the topic itself.

        The analysis is that brains are evolved systems built from at least the chemical level (if not, in fact, lower levels). Nature’s toolkit is biochemistry, so it’s not surprising other small-scale effects might obtain. Given how much we don’t know and can’t explain, who knows what we might uncover.

        “But the further down in intelligence we go, it seems like the stronger our interpretation of the behavior has to be to see it as report…”

        Yeah, maybe so, but consider what I said: “Dog, I think, have a form of self-reporting, and so do the higher primates. I wonder about elephants, crows, octopuses, and cetacean, too.”

        So I don’t see that as responsive to what I said. Our discussions should not be about what other people say. They should be about what we say.

      • SelfAwarePatterns

        On math, Stephen Wolfram has actually advocated a complete change in how math is taught. He argues that students should be given high level tools and allowed to solve problems with them first, and then taught the underlying mathematical principles. Of course, he’s advocating for something that would be good for his business. But I do think that approach, if it had been available, might have worked better for me.

        On quantum consciousness, sure, evolution might have pulled in anything from nature to accomplish what it does, but as I noted in the other half of my remarks, it’s not where the data currently points. Of course, that could change at any time, but if history is any guide, the surprises not currently in the data are unlikely to match our other preconceived ideas.

        I actually thought I was addressing what you said on self report. I’m not entirely convinced dogs do true self report. They are a social species, so it’s conceivable. But I think true self report requires metacognition, and the evidence for that outside of primates seems controversial. Even among non-human primates, it seems pretty limited compared to humans.

      • Wyrd Smythe

        I think Wolfram has a good point, although I agree it might be biased towards selling his own product. Showing students why math is so cool, and what it can do, is a good start, though. It’s a bit like what my parents did to me when I was a child. They read to me, but didn’t make any effort to teach me to read. When I started school, I was eager to gain the skill that would give me access to reading. Create the thirst — then show how to slake it.

        “…as I noted in the other half of my remarks, it’s not where the data currently points.”

        Said pretty much everyone to Copernicus. 😀

        The unknown is… unknown!

        “I’m not entirely convinced dogs do true self report.”

        Which is why I said, “have a form of self-reporting” — by which I meant they communicate their opinions and feelings to us. More to the point that they have opinions and feelings to communicate.

        In fact, with dogs, I think they might have evolved to communicate more than other animals due to their proximity and intimacy with us.

        This about dogs is they’re pretty transparent and honest about their feelings. Humans might find reasons to be less than 100% honest with researchers for whatever those reasons might be. Dogs have no reasons. 🙂

        Funny thing about Amos. He’s my favorite character — the one I identify with. I totally get that guy. OTOH, I don’t always get Holden. Or Naomi. (Alex is easy. Totally get that guy, too.)

        One thing about book 6. We never hear from Philp again. During the Revolution, Naomi encounters some people that help her, and at one point I thought one of them might turn out to be Philp, but nope, he’s just vanished.

      • SelfAwarePatterns

        Copernicus’ model was a more elegant solution to the data as it existed at the time. People just thought the ontology was too absurd to be true. But it was far more rigorous and data driven than quantum consciousness.

        I think it’s definitely plausible dogs evolved to communicate more with us, but as you noted, they don’t seem to have a lot of volition with that communication.

        I’m the same way with Philip. I keep expecting him to show up. Maybe in the last book.

      • Wyrd Smythe

        Amigo, the point of the Copernicus metaphor is that arguments about lack of evidence aren’t strong. Exactly as you say, Copernicus’s model was rigorous (and simpler than epicycles) — the point there is that it’s the arguments that matter.

        “[Dogs] don’t seem to have a lot of volition with that communication.”

        You state that as if it were an objection, but I don’t follow why it would be? If anything, as I said, that transparency might be seen as a plus — an honest indicator of the dog’s state of mind. I don’t follow what you’re objecting to?

        Bringing Philp (Filip? I forget) back in book 9 would seem almost weird. Although one could hardly complain — his absence does seem almost remarkable. Like he ought to reappear; maybe in a crucial moment? Saving his mom, maybe? (Too obvious?)

        I mentioned being vaguely bothered by the 4D (?) quantum aliens. It’s almost a bit too Star Trek somehow. But then this is space opera…

      • SelfAwarePatterns

        I do think lack of evidence is important. The possibilities beyond the data are vast. Reality seems like an infinitesimal slice of those possibilities. That seems to make the probability that loose speculation just happens to be the right guess, well, infinitesimal.

        On dogs, it seems like we’re drifting away from the original topic, whether they do true self report. I think lack of volition weakens the case. But I fully admit it depends on how loosely you want to define “report.”

        On multidimensional aliens, yeah, I think we’ve talked before about its ghost story aspects. If you look at the history of space opera, there’s always been a strain of that. In many ways, they’re just as much a fantasy as anything involving wizards and elves. It’s just that this particular type of fantasy has the trappings of science around it to varying degrees.

      • Wyrd Smythe

        “That seems to make the probability that loose speculation…”

        “Loose speculation”? See, to me that’s either ad hominem or irrelevant, since you’re either suggesting I’m engaged in loose speculation, or you’re talking about someone else entirely. (Hopefully the latter! 😉 )

        Regarding lack of evidence, my only point ever is that one should not be too committed to a point of view that lacks evidence. (Honestly, from my perspective, I keep gnawing at these bones because I’m trying to get you to be a bit more provisional in your commitment to things like MWI and strong computationalism. I’ve long been struck by the contrast between your skepticism on some topics, but not others. If nothing else, I seek to understand it.)

        I certainly grant the point that loose speculation has a low chance of success, but that doesn’t apply to anyone at this party. 😀

        “On dogs, it seems like we’re drifting away from the original topic, whether they do true self report.”

        I already replied: “Which is why I said, “have a form of self-reporting” — by which I meant they communicate their opinions and feelings to us.”

        You replied they lack volition, and I asked what that had to do with it.

        FWIW, I would define “true” self-reporting as the ability to directly answer questions about one’s mental state. All I mean about dogs is that their mental state (such as it is) is pretty apparent. (And, further, given all we know about dogs, I think we can trust that the apparent emotions are the same as, if simpler then, ours. So when a dog is apparently happy, I think we can take that as a form of report.)

        “It’s just that this particular type of fantasy has the trappings of science around it to varying degrees.”

        Very true. At some point reading I was thinking along those lines that for a “hard SF” series it sure has a strong fantasy component. Damn near wizards and elves. Protowizards, I guess.

        Not quite as far over the edge as Star Wars, though. 🙂

      • SelfAwarePatterns

        On loose speculation, I’m referring to the purveyors of quantum consciousness. The more responsible advocates engage in speculation only loosely, at best, motivated from the data. The adjective “loose” here refers to having lots of assumptions beyond that data. The less responsible ones veer into outright pseudoscience.

        I’ve noted many times that I see the MWI as a candidate for reality, albeit one I find promising. So if your goal is to have me not be absolutely committed to it, relax, I’m already there. But if your goal is to have me reject it? Sorry. I can’t see that as warranted, at least not yet.

        On computationalism, also sorry. We just have to live with disagreement here.

        I would describe The Expanse about as hard as traditional literary space opera, which itself is far from diamond hard. It tends to be more grounded with the human tech, and looser with the alien stuff. But literary space opera, as a whole, tends to be a lot harder than the vast majority of media space opera, which is why I see the TV show as substantial progress.

      • Wyrd Smythe

        “On loose speculation, I’m referring to the purveyors of quantum consciousness.”

        I had to go back to see where this started, because how did we get onto quantum consciousness? From talking about The Expanse!

        That found its way into the debate attractor about speculation.

        As I mentioned at one point, for me that attractor exists because I’m trying to understand the razor you use to determine what ideas to be skeptical about and what ideas to accept as viable. MWI is an example. My arguments don’t seem to move your needle at all. I feel my arguments are strong enough to warrant at least some skepticism. (Maybe what drives me is just wanting to know why you find my arguments so easy to ignore. I feel they’re strong arguments!)

        As far as quantum consciousness goes, honestly I see it as similar to Greg Egan’s books on computational consciousness. Both are currently SF. Both are currently speculation. I don’t see data directly pointing to either one. Both certainly warrant skepticism. I do see things that are suggestive.

        “So if your goal is to have me not be absolutely committed to it, relax, I’m already there. But if your goal is to have me reject it?”

        Ha! I think there’s plenty of comfortable ground between those extremes. I’ve never advocated for anything other than some healthy skepticism and acknowledgement of what I’ve called a Big Ask. (In the previous comment I said, “a bit more provisional.”)

        But at least we can agree on The Expanse! Very true about the TV version.

      • SelfAwarePatterns

        ” I’m trying to understand the razor you use to determine what ideas to be skeptical about and what ideas to accept as viable.”

        That’s a good question. For me, I start with what the mainstream science is saying and why it’s saying it. If I have doubts about that it’s saying, I try to understand why those doubts may be misguided. If there is debate between various alternatives, what are the arguments for and against the various options?

        I have no illusions about my personal expertise. But as I posted recently, I also have no illusions about the expertise of my fellow amateurs. When we think we’re seeing something an entire field of scientists are missing, it’s far more likely we’re just making basic mistakes.

        In the case of MWI, I hated it when I first heard about it. It seemed insane. But as I read more about QM, I realized that all the options are either insane or incomplete. What made a difference for me, was reading a Quanta article a few years back that was a long sustained attack on MWI. I found the arguments underwhelming, akin to (sorry) the arguments I used to hear for God’s existence, and wondered if that was the best available. So I dug. I found, like most long term interpretations, it was far harder to dismiss than I liked.

        My issue with most of your arguments is you don’t seem to really take the MWI seriously, so you don’t give it a chance to work through your concerns. Or they’re in the “This is just nuts!” category, which as I said is true for all QM realist options. And if it was as easy to dismiss as you describe, I guarantee many physicists would have seized on what you take to be strong arguments decades ago to kill it off. Remember, just about everyone hates the MWI when they first hear about it. The overwhelming majority who accept it do so only grudgingly.

        It might still turn out to be wrong. Maybe someone will discover an actual objective collapse. Or find conclusive proof that the wave is an illusion. If so, that will be just as insane, because then we’ll have to figure out how this action at a distance thing works, and how to reconcile it with relativity. Or maybe we’ll find that the core Everettian physics is accurate, but that something else kills off the other branches. I’ve tried to learn more about quantum Darwinism, but I can’t ever seem able to get a clear description of it.

        Anyway, that’s my thinking. Hope this helps.

      • Wyrd Smythe

        I agree with nearly all of that.

        “In the case of MWI, I hated it when I first heard about it.”

        We went different ways. I think I was young enough and steeped in SF enough that the idea appealed to me at first. It was only after thinking about it I found difficulties with the idea.

        The one thing I don’t agree with (as you might expect) is:

        “My issue with most of your arguments is you don’t seem to really take the MWI seriously, so you don’t give it a chance to work through your concerns.”

        Not true. I was fine with it when I first heard about it decades ago. It has only been through discussions over time that I found myself increasingly questioning it. It’s only recently that my skepticism has decisively won the battle. You are correct I find it hard to take seriously now.

        “Or they’re in the “This is just nuts!” category, which as I said is true for all QM realist options.”

        I don’t think that true, either, since my primary objection involves the energy question. That’s the issue I think is potentially a show-stopper and MWI’s most rabid proponent doesn’t have a good answer for it.

        I also think there are different levels of “just nuts.” QM forces us to accept non-locality (apparently), even in MWI. Superposition is weird, but makes a kind of physical sense in terms of wave behavior. The only really nutty thing is that non-locality and the apparent randomness of, for instance, which electron absorbs a photon. But even here there is a kind of physical sense to it — no known laws of physics are violated. (Even non-locality can’t be used for signalling, so it doen’t violate SR.)

        Contrariwise, MWI says new physical universes spring into existence because we measure a photon. Let’s be clear — it’s not that this violates (informed) common sense (although it certainly does). It’s that it appears to require new physics. Under current law, new things don’t spring into existence because of the behavior of a single photon.

        You skipped my post reviewing Carroll’s book, and I understand why you might have, but I covered all this there. Not having found what I sought in Carroll (some answers), I’m going to look into the work DeWitt did bringing decoherence into MWI. And I want to return to Everett’s paper. I do take MWI seriously and want to understand it

        One thing I know about myself is that, if I could find a convincing argument favoring MWI, I would change my thinking. But the only real argument for is “It’s just Schrödinger,” and there are some strong logical objections against. I would really like to understand why some people think that’s a fair fight.

        (Admittedly the probability argument is based on credibility. There’s a Sean Carroll out there who published a book proving MWI because his random photon device, and all its replacements, always gave 0s. And another one who’s getting all 1s. And Sean Carrolls getting all sorts of structured patterns (20 0s and 20 1s repeating forever, etc). Under MWI these all exist albeit vastly swamped out by the versions getting more “acceptable” results. That seeming beyond the pale is an intuitive judgement, although I would argue a reasonable one.)

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