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## 2018-09-02

## Channels

- # announcements (3)
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- # bangalore-clj (1)
- # beginners (88)
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- # shadow-cljs (162)
- # unrepl (4)

emacs users: what do you use to switch between buffers? `C-x o`

seems really slow if i need to switch backwards

`ido-switch-buffer`

seems nice http://ergoemacs.org/emacs/emacs_ido_mode.html
(I use another thing myself)

there's also https://github.com/dholm/tabbar , never tried it

will ido-mode be in conflict with stuff like helm

@U45T93RA6 thanks, I was confused because Emacs' default binding for `C-x o`

is `other-window`

.

I actually us S-arrows for buffer switching with ido: https://github.com/thatismatt/emacs.d/blob/master/init.el#L578-L581

oh man i actually meant windows!

lol đ

but i use `C-o`

to create empty lines

`C-o`

is nice, but lots of other emacs libs bind it, so I am forever having to unbind those... so it isn't ideal.

F keys maybe? (in which case, and if you use macOS, this is handy https://clojurians.slack.com/archives/C099W16KZ/p1535473832000100 )

I found it about the same usage compared with OpenJDK

Philosophical CS debate question: How is all maths and arithmetic not just geometry? For any arithmetic construction, we're essentially building a machine, where spatial relations of the mechanism always matter ("no, carry the one to the left, not the right!"). And for that matter, how can one have an intuition about a scalar number without at least an intuition of a 1D line anyway?

The spatial relations of the arithmetics may not exactly match 3D geometric intuition, but there's always *some* spatial relationship between each thing, perhaps along a 2D or 1D axis

yeah. I think that itâs often useful to find different ways of explaining the same problem/solution

most people have some sort of spatial intuition, so explaining problems in a way that relates to that can really help

Yeah, my hunch though is that all algebraic intuitions are also geometric. Associativity, transitivity.. They're always constructed in relationship to order and placement of elements on a page. And the position of them matters.

Like, associativity in algebra and reducing terms, carrying relations back and forth. We're operating over our idea of the arithmetic machine, and that things can be carried back and forth.

I think itâs useful to draw a distinction between geometry, the field and the representation of a problem

Yeah, they're sensibly distinct subjects in my mind too. Definitely a useful distinction

"carrying" is an artifact of a particular algorithm for addition. it is not innate to addition itself

You could probably argue that all geometric relations can be represented in algebraic ones.

But my suspicion is that we're all using geometric intuitions to construct those algebraic relations

doing calculus recently with someone and it was entirely divorced from any intuition

the "carrying" algorithm for addition is symbolic manipulation. we aren't thinking of lines in a plane and how they combine. we are going over rules for symbols

Any symbolic manipulation is going to assume some geometric relationships between the symbols, afaict

that seems to me to mistake where the insight lies. just because it is written and physical doesn't mean that the insight into something is physical. the symbols `d/dx(3x) = 3`

doesn't use any geometric transformation. we aren't analyzing bezier curves. we could switch the symbols and it would not cloud our thinking. the insight is in the abstraction of functions and algebra, not in handwriting

It may be one of those yin/yang things. Form and function. People always debating which side is more fundamental đ

From my perspective, any algorithm or equation you present, there will always be some spatially analogous transformation you're using to operate over the terms to arrive at some result

And some spatial transformations are analogous to others, so we end up with a bunch of spatial shorthand operations

We could add all the apples using ones, moving them around directly in space. But instead we put them in a line and give symbols to represent collective amounts of them, like 8 apples and 9 apples. Then we take those and put them in an automaton we call arithmetic, where if you move the things this way and that way, and carry the one, etc, you get the resulting number of apples you want. But that other transformation was still a spatial one, just over a more condensed analogous space. It was just a more general set of spatial relationships that we know are analogous, and we know one is more efficient than another.

Arithmetic is a 2D, 10 State automaton, with neighborhood rules specific to some columns and rows.

But, I'll grant you that the algebraic relationships may be just as... *fundamental* as the geometric ones.

this is russels paradox. Let R be the set of all sets which are not elements of themselves

if R is a member of itself, then by the definition, it is not a member of itself. If it is not a member of itself, then it meets the requirements of the rule that determines what is a member of itself

we can use heuristics and simple models to think of it but those are simply crutches. the idea is not based in geometry

But we can construct shapes in a certain number of dimensions that are paradoxical (incorrect) when translated into another set of dimensions

When a 2D picture is trying to represent a 3D shape, it can be paradoxically wrong about the feasibility of that transformation.

again I think youâre conflating the way we can represent a problem with something fundamental about the problem

The semantics of the automaton in which Russel's expression was operating in are allowed to make expressions that fail to map to other geometric intuitions

just because we can represent a problem visually, doesnât mean it has to do with geometry

I guess we're touching on the subject of whether truths exist as platonically disembodied objects, non-contingent on time and space. The whole Platonic vs Aristotelian interpretation

i don't think so. i thought you were saying you could essentially draw all of maths and it was a deep truth

Well, to the extent that a 3D geometric operation can be compiled down to a simplified 2D geometric operation over an automaton

As someone who has mostly studied math, I tend to agree with @dpsutton here. The progress we make when putting our reasoning in written form stems mostly from having a symbolic notation on a hard external medium - so it's symbolics more than it is geometry which are essential here. I could imagine a blind mathematician using touch, not sight, for this purpose. Granted, many mathematical intuitions are visual - but we tend to use writing (especially calculus) to make mechanical progress where our intuition cannot get us any further. What's beautiful with practicing maths IMHO is that it can expand your intuition to new territories, in particular ones which are not well captured visually.

Quoting Von Neumann: "you don't understand math, you get use to it."

For the record I'm not trying to disparage one view point over another. Maybe I'm arguing that geometry is a little under appreciated, but I'd agree future progress is in understanding heavier maths. But I just can't help but see calculus as yet another automaton. Spatial operations that are conveniently more efficient than the spatial operations they analogize.

Sure, and if you can discover or promote ways in which geometry can fuel intuition I certainly won't deter you from that đ

I always thought maybe some low hanging fruit was in those magic maths, where you get some arithmetic shortcuts for certain factors in certain bases.

And maybe you could exploit it using a fast base conversion scheme. Not sure if that comes from a geometric intuition though.

Most "real" maths tend to ignore residuals and fingerprints associated with clusters of number patterns in particular bases, right?

I guess it's slightly based on a geometric intuition: step outside the arithmetic axioms and exploit the invariant patterns that are incidental to the local neighborhood

i don't know what residuals and fingerprints are but they sound like numerical analysis might care about that kind of stuff. The thing i see from you is a lot of enthusiasm but just making these sweeping statements about invariant patterns and local neighborhoods. I don't know what you are trying to say. I think you should spend some time with some textbooks and refine what you want to say

But it's not a bad idea. Basically, neighborhoods of numbers produced by arithmetic of a certain base will have information patterns in the numbers that are not exploited under the normal rules of arithmetic. You know the common ones: add up the digits of any 10 base number and if they equal 3, 6 or 9, then you know it's divisible by 3. Well, that's an artifact of base 10. If we all used base 50 instead, then we could add numbers together to see if 7 goes into them. Because 49 in that case is base-1.

But there's lots of other examples where different incidental relations between the numbers can be exploited

I'm not sure right now, but I think you can come up with a rule like that for numbers written in any base, and asking whether they are divisible by any integer N.

Some of them only need to look at the few least significant digits, others need to take all of the digits into account.

But there's probably some magic math way to base convert by exponential steps. Then just stepwise to your goal.

How about an arithmetic where every number had an imaginary/complex component as its base. So various numbers in different bases can coexists. Or even a single number can be *represented* internally by numbers of various bases, like `1,08(23b16),(86b23)59`

So the above would be said, "one million, eighty twenty-three base sixteen thousand, eighty-six base twenty-three hundred and fifty nine" đ

You can of course represent numbers in a wide variety of ways other than the typical "base B" notation. You can think of hours, minutes, and seconds as a "variable base" notation if you squint hard enough, e.g. hours are base 12 or 24, minutes and seconds are base 60.

I'm sure there are some applications where alternate representations of numbers would give an advantage in computation speed, but I haven't worked with any of them enough to give examples.

Yeah, I've considered `((15)(19))`

for number/base, so that you could even express a base as composite too `((15)((13)(16)))`

But I wonder what that nested base lambda notation would look like with only binary numerals representing the numbers and their bases

I think I'd prefer the base to the left too, so it fits better with reduce and lambda semantics

Like, you could represent the number 168 in base 50 as `((50)(3)) ((50)(18))`

. Just add 3 and 18 and you get 21, which we already know is a multiple of 7 in base 50 (like 9 and 6 are to 3 in base 10)

And with respect to residues, for instance any 1 divided by 13 is 0.07692307692. That `076923`

keeps repeating and when 13 interacts with other numbers, it tends to leave that fingerprint in lots of places. Some other primes also have their own "signatures" with respect to base ten. In base 13, obviously, that signature washes away. In other bases, it might also not show itself. And certain bases will show certain traces of certain primes left behind in their computations. Also an avenue of exploitation.