It reminds me of that painting “this is not a pipe” what is it? It’s a _picture_ of a pipe.

Shouldn't be too hard to 3D print addiators in any base. I've never seen models online but it would be a cool project. I can imagine writing some python in blender that could output STLs for any base you like.

@@ChrisStaecker This would be so cool!

@@ChrisStaecker Well, there goes my weekend.

I’m interested if you come up with anything!

@@ChrisStaecker probably not python in blended, but openscad with parametric design.

Yeah it literally looks like a bootleg addiator

*O R I G I N A L*

Gotta get a 1d16

Probably you had the adductor- very easy to get nowadays on eBay!

I often make my quizzes out of 12 points so I can easily deduct half, third, or fourth credit. Students don't like it though! They get 7/12, but then need to convert to a percentage to find out their "real grade".

i recently bought an addiator for the pre-decimal British currency. It works great with £sd, But I can't find a Hexco or IBM addiator that works with hexadecimal numbers like the one you have here. They can't all have been thrown away. Someone must have one at the back of a dusty drawer. Please get searching folks!

Thanks! The sliding up isn’t really any kind of complement- it’s more of a direct subtraction. Sliding down makes it add, and sliding up is just the opposite which makes it subtract. (Typical subtraction by complements would move the mechanism in the same direction as adding, but suppress or modify the carry to make the details work out.)

I agree 6 digits is a bit weird- maybe just copying the addiator? In decimal, 6 digits gets you "up to a million", which seems natural I guess. To me the hex adder is very long and skinny- making it slightly wider to 8 digits would've been fine.

Possibly copying the Addiator model? Hexadecimal is commonly pronounced as hex for short which is technically 6? 6 hex digits will get you to 16,777,215 in decimal which is probably high enough for what you'd use it for?

Yes- this was the only other old school hexco product I could find. Any others? Possible for a video some day.

True, but I do not regret at all searching for a Monroe L-Series. I use it in place of computer-based methods frequently.

The choice of base doesn't effect the theorems at all. (Except the very few theorems which are specifically about base 10 expressions of numbers.) The base only determines what the number looks like when we write it, but not what its properties are. A number is even or odd, prime or not prime, etc- these are properties of the number itself and don't change depending on the base. For this reason, facts which are specifically about base 10 descriptions of numbers are generally regarded by mathematicians as unserious. Other-base mathematical cultures would eventually realize the practical importance of binary for machine computation, so a preference for binary in technical contexts is probably universal.

Perceptive question! The mechanism can't handle double-carries. The Hex Adder handles this exactly like the addiator- see my addiator video around 3:10: kzfaq.info/get/bejne/aNOmZ5iJtZqckoU.html I shot about 30 seconds for this video explaining it, but I ended up cutting it.

Ive wondered about this too, It almost depends on what you define your "tryte" as, the trinary version of the byte. I got b27 to work and used 0-9 and letters A-Z to, almost work, at one point I think i used greek numerals. I was working in balanced ternary though

Never heard of this- I’m interested!

@@ChrisStaecker Sorry; I just made it up. Would be cool though.

Tom!

I think there were only ever ternary computers though, nothing higher (other than analog computers), so not too many shades of grey

yeah and they might be bringing back analog computers according to a veritasium video (because they can apparently do the multiplications used in neural networks more efficiently than digital computers)

Yes- I've heard of ternary machines in the USSR. Wild!

They even made base 5 machines too (It was called Biquinary), where they used a few bits to encode a group of 5, and then used another one one the left to determine which range of 5 it was in. Quite interesting to read about

@@lapatatadelplato6520 Interesting- the standard chinese abacus (suanpan) is also called biquinary because each digit has a base-5 piece, and a base-2 piece.

I don't know of any modern instrument based on the troncet (addiator-type) design.

Way out of my price range! Unless you know a guy...

@@ChrisStaecker If I can make another suggestion what about a Line of Chords ruler. My favourite workshop tool.

@@ChrisStaecker I don't know a guy but I'm sure one of your hardcore fans can make a plan.

​@@brendtkieffer7095 I've never heard of this but i will have to look into it. I've been planning a video about the sector rule for a long time, which looks similar. Thanks for the tip!

@@ChrisStaecker It's out of my price range too, but I'd kick in $20. If enough people did, you could have a Curta.

I'm not really sure- that image comes from here: commons.wikimedia.org/wiki/File:Ms.Thott.290.2%C2%BA_150v.jpg You can see elsewhere on the page the numeral for 5 being treated strangely. I guess these are just two variations on the glyph? I can't find more info.

Okay thank you very much. What happens when you carry over to an F on the machine? Thanks in advance.

@@YamamotoTV2021 A "double carry" is a bit tricky on a machine like this- I didn't get into it in this video, but I discuss it in detail in my addiator video. See around 3:08 here: kzfaq.info/get/bejne/aNOmZ5iJtZqckoU.html

There are also even weirder bases: for example complex bases or rational bases.

@@pdote Base _i_ is a weird one for sure. But yeah, all positive and negative integers can be represented as a positive integer in base -x. Meaning all the positive and negative numbers are represented twice, if you include the negative numbers in that base as well. Kind of disproves the idea of 'bigger infinities', at least infinities that are bigger in a countable way.

I truly believed base -1+i was the future at one point. Since used only zero and one I encoded it with hex digits. Had a hard time getting division to work. I eventually left that project for geometric algebra. It was a weird experience graphing things in 4 dimensions. Balanced ternary is gorgeous if you get s chance to see it.

Yes- what a number looks like in a specific base is not often very helpful in mathematical settings. I can't think of many examples, but one favorite is that the Cantor Set is easy to describe in terms of base-3 numbers, and very complicated to describe in base-10. But 99% of the time it doesn't matter.

@@ChrisStaecker Bases of numbers are useful of course, but they are something more like coordinates - in fact you can think of the carrying operation by constructing an algebra of polynomials with natural number coefficients. The base ends up being something you stick in the variable to evaluate the number.

Never heard of him! I guess it's a pretty obvious gag though- I've heard something similar from Adam Neely.

Yeah this guy 2:24

Now I want to make some base 12 Rugen’s Bones.

As someone working construction in the US of A, I love 12! So divisible!

$25

Do you disagree that most humans have used base 10? This certainly must be true if we count person-by-person since modern humans are far more populous than in the past. But even if not, is there any real argument? Obviously I chose my examples to support my point, but which am I missing? I'm aware of historic sexagesimal systems (which are still based on 10s, together with 6s), and some duodecimal systems for counting certain things. But base-10 counting has arisen independently in world cultures many times, right? (I'm not an anthropologist) I can't possibly believe that the choice of base 10 is to facilitate machine calculation- this is a concern that developed long after cultures had already decided how to group their numbers.

@@ChrisStaecker Nevermind that it's futile to come up with based statistics of how common different systems were throughout pre-modern history and decide which system was "the most" used, and for many reasons. (which alone makes the initial claim unfoundable) If we go by historical evidences alone, disregard lesser-known systems, and only include those that are *at least somewhat* used to this day without special aids: Binary is used all the time, certainly if you ever ordered in pints. Base-3 is one of the more natural and intuitive groupings a human can perceive, also a tsp is a third of a tbsp. Base-6 whenever you roll a dice (can't say "two dies" without base-6) Base-7 for weeks (can't say "couple of weeks" without base-7) Base-12 for time and calendar ("couple of months", AM/PM time system) Base-24 again for time ("couple of days") Base-60 yet again for time ("half a minute" is base-60) Base-360 for degrees of angles (you could argue it's also pi but i think it's fair to say most often when someone thinks of quarter of a circle, or a right angle, they're thinking 90 degrees rather than half-pi but speaking of which base-pi is not uncommon for this use) I completely disagree with your claim that base-60 and base-100 and other bases which are multiples of 10 are duplicates of a small base by x10ⁿ. Regardless of notation, which as you said in the finale of the video is mere representation of an idea, the different base systems are used for their meaning whereby the base-n stands for a single whole (or, drumroll, "100 per *cent*"). Anything less than that whole is part of it - a tenth, a quarter, a third. While any multiples of that whole are counted as multiple wholes. You'd have to do a whole lot of convincing to probably anyone who uses seconds-minutes-hours system that a minute *means* "ten six seconds" or "six ten seconds", rather than it means "sixty seconds". If you said "half a minute is three ten seconds" it might be perceived as funny in some circles, but only because it's contrary to the common meaning of a minute. Therefore the 60 in a minute is the whole, and that's why it's base-60. In the same way "two minutes" don't mean "twelve ten seconds", rather they're "two sixty seconds". So I didn't bother you with a list that includes base-100, 1000, but to claim these bases are irrelevant would be very contrary to the way numbers are used by people (and mathematicians) for millennias. And if I already mentioned base-1000, then you can probably guess what I think about base-1024. And yes I know you can represent all of these with "x10ⁿ" but like you said numbers are an idea beyond the representation of them, reducing every multiple of 5 to base-10 is falling for the exact fallacy you warned against.

@@pubcollize I think I disagree, though what you say is interesting. I think I believe in true duodecimal systems, but I can't really imagine sexigesimal as a non-subdivided true base-60 system. The Babylonian symbols for writing sexagesimal numbers are clearly based on 6x10. It seems to me that a pure base-60 system with 60 different symbols per digit would be totally unusable for people. Our use of base 60 in time and angle measurements is only workable because we write those numbers in a more understandable base. (Though I agree that people don't really think of 60 minutes as composed of 6 groupings of 10 minutes.) Anyway thanks for the comments-

@@ChrisStaecker Some bases divide better than others. For example, 1/7 in base 10 is a pain. It has a nice cyclical pattern, but it's incredibly cumbersome to use. Some bases are better at this than others. For example, even though in base 16 there are fewer nonrecurring reciprocals of integers, their recurring nature is easier to use than that of 1/7 in base 10. (All the reciprocals of the integers below 20 have single or doubly recurring hexadecimal expansions, which is really good.) The best base that I have seen for this effect is base 6. For all the reciprocals of integers below 20, 9 of them terminate in base 6. 8 of them have easy to use recurring expansions(where it recurs with a "width" of 2 or fewer digits). The only terrible ones are 13, 17, and 19. So, I would say that in all honesty, from a pure ease of use standpoint, base 6 makes more sense. Oddly enough, very few cultures use base 6 though.

@@ChrisStaecker If we only count base systems based on the number of unique symbols they have then the roman nonpositional system would be base-7, and most duodecimal uses we're familiar with would be base-10. With all due respect it doesn't make much sense. Sorry if I'm misrepresenting what you meant. Either way it again falls to the same problem of giving too much weight to the glyphs than to the ideas.

That's a pretty trippy animation!

Yes! Me too! I loved that one. It was the trippiest psychedelic my 5 yr old brain could have. So cool.