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Posts tagged with philosophy

The discovery of the laws of numbers is made upon the ground of the original, already prevailing error, that there are many similar things (but in reality there is nothing similar), at least, that there are things (but there is no “thing”). The supposition of plurality always presumes that there is something which appears frequently,—but here already error reigns, already we imagine beings, unities, which do not exist. Our sensations of space and time are false, for they lead—examined in sequence—to logical contradictions. In all scientific determinations we always reckon inevitably with certain false quantities, but as these quantities are at least constant, as, for instance, our sensation of time and space, the conclusions of science have still perfect accuracy and certainty in their connection with one another; one may continue to build upon them—until that final limit where the erroneous original suppositions, those constant faults, come into conflict with the conclusions, for instance in the doctrine of atoms. There still we always feel ourselves compelled to the acceptance of a “thing” or material “substratum” that is moved, whilst the whole scientific procedure has pursued the very task of resolving everything substantial (material) into motion; here, too, we still separate with our sensation the mover and the moved and cannot get out of this circle, because the belief in things has from immemorial times been bound up with our being. When Kant says, “The understanding does not derive its laws from Nature, but dictates them to her,” it is perfectly true with regard to the idea of Nature which we are compelled to associate with her (Nature = World as representation, that is to say as error), but which is the summing up of a number of errors of the understanding. The laws of numbers are entirely inapplicable to a world which is not our representation—these laws obtain only in the human world.

Fried Rice Nietzsche. Human, All Too Human

Like Spinoza, Nietzsche thinks about something for a bit and decides whatever conclusion he came to must have been the correct one. Learn something before you open your mouth, fool.

Yes, it’s ultimately futile to try to make a comprehensive comparison of things. Ultimately nothing is the same. But you know what? We don’t need to be so picky. Or rigid. Even though every rock is unique, they’re all comparable in some ways, like for example, they all fall under the category of “rock”. So I can put them in an equivalence class for the time being—without robbing them of their unique individuality, just saying they are comparable without being identical.

I feel like I’m stating the obvious. And this person is a venerated Western intellectual? Give me a break.

 

If by the “laws of numbers” he means to undermine mathematics, then Nietzsche’s critique falls short of most interesting mathematical stuff.

http://upload.wikimedia.org/wikipedia/commons/c/ce/Universal_property_tensor_product.png

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|3,2,1>+|3,1,-1> Orbital Animation|4,1,0>+|4,3,3> Orbital Animation
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Electric field of 3 point charges
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http://math.ucr.edu/home/baez/pentacontihexahedron3.jpg


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http://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/Symmetric_group_4%3B_Cayley_graph_4%2C9.svg/1000px-Symmetric_group_4%3B_Cayley_graph_4%2C9.svg.png

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http://math.berkeley.edu/~teichner/Bottoms/IHX.gif

Reine geometrie

We don’t “lose” the insights from the A→B process because, in Fried Rice’s opinion, there’s some problem with counting things.

Yes, not all rocks are the same. But. We can still make equivalence-classes of rocks—treating them as the same for the time being.

And even if you couldn’t—that wouldn’t change the weirdness that happens when you mix two things like plus and times

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(you get prime numbers which show up at not-totally-predictable times)

PrimeSpiralGrid

PrimeSpiral

Prime spiral

PrimeSpiralHexagon

…or what happens when you combine shifts and swaps:

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Nobody is “making this up”. Nor does it depend upon some person’s viewpoint. You can work out the symmetric group of order 3 and you’ll find the same thing I found when I worked it out.

This crap is just like what I’ve seen of Rousseau, Spinoza, Hegel, even Leibniz. People so full of themselves they think every time they clear their throat someone should get out a pen.

Remember that this is the same bloke who posited in The Eternal Return that states-of-affairs must recur given an infinite amount of time. Which is wrong: dynamical systems can wander off and never come back, like a random walker in 3D.

To me it’s much worse to invent false histories or pretend to authority than to suggest we treat a handful of rocks as equivalent for-the-moment. Get off yourself, Nietzsche.




1. The monad, of which we will speak here, is nothing else than a simple substance, which goes to make up compounds; by simple, we mean without parts.

2. There must be simple substances because there are compound substances; for the compound is nothing else than a collection or aggregatum of simple substances.

Gottfried W. Leibniz, Monadology

 

Crazy how a “father” of calculus was so illogical in his seminal work of 1714.

  • The existence of compound things does not imply the existence of partless atoms.
  • He asserts, doesn’t prove, that a compound is “nothing more than" a collection of simple substances. (atoms)







I’ve collected a few tidbits about non-wellfoundedness on isomorphismes:

  • the opposite of the idea of “indivisible atoms" at the "bottom" of everything
  • turtles all the way down
  • (infinite regress is OK)
  • a > b > c > a
  • (so the two options I can think of for non-wellfounded sets are either an infinite straight line or a circle—which biject by stereographic projection)

as well as examples of irreducible things:

  • if you take away one Borromean ring
    http://upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Borromean_Rings_Illusion.png/774px-Borromean_Rings_Illusion.png
    then the whole is no longer interlinked
  • Twisted products in K-theory are different to straight products.
    https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/M%C3%B6biusStripAsSquare.svg/1000px-M%C3%B6biusStripAsSquare.svg.png
    A Möbius band is different to a wedding band.
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    Yet 100% of the difference is in how two 1-D lines are put together. The parts in the recipe are the same, it’s the way they’re combined (twisted or straight product) that makes the difference.

So Leibnitz’s assertions are not only unsupported, but wrong. (Markov, causality, St Anselm’s argument, conservation of mass, etc. in Monadology 4, 5, 22, 44, 45.)

tl,dr: Leibniz, like Spinoza, uses the word “therefore” to mean “and here’s another thing I’m assuming”.




We often speak of an object being composed of various other objects. We say that the deck is composed of the cards, that a road is [composed of asphalt or concrete], that a house is composed of its walls, ceilings, floors, doors, etc.

Suppose we have some material objects. Here is a philosophical question: what conditions must obtain for those objects to compose something?

If something is made of atomless gunk then it divides forever into smaller and smaller parts—it is infinitely divisible. However, a line segment is infinitely divisible, and yet has atomic parts: the points. A hunk of gunk does not even have atomic parts ‘at infinity’; all parts of such an object have proper parts.




A plant that turns toward the light, or a worm that writhes after severation, doesn’t do so out of free will.Their internal biochemistry mechanically responds in a deterministic (if stochastic) way. They don’t make choices.
In Vehicles, Valentino Braitenberg asks if we humans aren’t the same way.
 
Even I could come up with the easy arguments for stimulus→response:
something annoys me → bad mood → don’t pay attention to the car that’s pulling out → accident
physics says so
I read a compelling book about robots → inspired to go to graduate school and dedicate my life to synthetic consciousness → entrenched in a career with no prospects
people predictably respond to stimuli: we avoid people & situations we don’t like and gravitate to what we do like (subject to feasibility constraints).
 
But Braitenberg does something much more convincing. He builds robots to prove his point.
He starts by resolving the problem of Burridan’s Ass stochastically. A phototropic robot might be stuck at θ = 0° between two light sources, but since we can’t get it to exactly 0° the robot—without free will or choice—heads toward one of the “bales of hay”.

What seemed like a paradox according to pure thought went away when someone took the paradox seriously enough to build a physical model. 
That problem is resolved with two wires connecting two stimuli to two engines. As the book progresses Braitenberg builds more lifelike robots using more connections—complex networks that reroute external stimuli to mechanistic, deterministic robotic response.

Braitenberg doesn’t get all the way to the dramatic complexity of "I love you! … I know." but given what’s possible with a few tens of connections, what could be possible with hundreds of trillions of connections?

Because of this book I went through years of my life believing I was probably an automaton.

A plant that turns toward the light, or a worm that writhes after severation, doesn’t do so out of free will.
image
Their internal biochemistry mechanically responds in a deterministic (if stochastic) way. They don’t make choices.

In Vehicles, Valentino Braitenberg asks if we humans aren’t the same way.

 

Even I could come up with the easy arguments for stimulus→response:

  • something annoys me → bad mood → don’t pay attention to the car that’s pulling out → accident
  • physics says so
  • I read a compelling book about robots → inspired to go to graduate school and dedicate my life to synthetic consciousness → entrenched in a career with no prospects
  • people predictably respond to stimuli: we avoid people & situations we don’t like and gravitate to what we do like (subject to feasibility constraints).
 

But Braitenberg does something much more convincing. He builds robots to prove his point.

He starts by resolving the problem of Burridan’s Ass stochastically. A phototropic robot might be stuck at θ = between two light sources, but since we can’t get it to exactly the robot—without free will or choice—heads toward one of the “bales of hay”.

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What seemed like a paradox according to pure thought went away when someone took the paradox seriously enough to build a physical model

That problem is resolved with two wires connecting two stimuli to two engines. As the book progresses Braitenberg builds more lifelike robots using more connections—complex networks that reroute external stimuli to mechanistic, deterministic robotic response.

image

Braitenberg doesn’t get all the way to the dramatic complexity of "I love you! … I know." but given what’s possible with a few tens of connections, what could be possible with hundreds of trillions of connections?

image

Because of this book I went through years of my life believing I was probably an automaton.


hi-res




I am a philosophical naïf with the background knowledge of the typical economist; that is, “utilitarianism is the moral framework, Rawls said some stuff that disagreed, but what can you really do with that stuff? Now tell me your R-squared.




Transgressing boundaries, smashing binaries, and queering categories are important goals within certain schools of thought.

Reading such stuff the other week-end I noticed (a) a heap of geometrical metaphors and (b) limited geometrical vocabulary.

What I dislike about the word #liminality http://t.co/uWCczGDiDj : it suggests the ∩ is small or temporary.
— isomorphismes (@isomorphisms)
July 7, 2013

In my opinion functional analysis (as in, precision about mathematical functions—not practical deconstruction) points toward more appropriate geometries than just the [0,1] of fuzzy logic. If your goal is to escape “either/or” then I don’t think you’ve escaped very much if you just make room for an “in between”.

By contrast ℝ→ℝ functions (even continuous ones; even smooth ones!) can wiggle out of definitions you might naïvely try to impose on them. The space of functions naturally lends itself to different metrics that are appropriate for different purposes, rather than “one right answer”. And even trying to define a rational means of categorising things requires a lot—like, Terence Tao level—of hard thinking.

I’ll illustrate my point with the arbitrary function ƒ pictured at the top of this post. Suppose that ƒ∈𝒞². So it does make sense to talk about whether ƒ′′≷0.
But in the case I drew above, ƒ′′≹0. In fact “most” 𝒞² functions on that same interval wouldn’t fully fit into either “concave" or "convex”.
So “fits the binary” is rarer than “doesn’t fit the binary”. The “borderlands” are bigger than the staked-out lands. And it would be very strange to even think about trying to shoehorn generic 𝒞² functions into
one type,
the other,
or “something in between”.
Beyond “false dichotomy”, ≶ in this space doesn’t even pass the scoff test. I wouldn’t want to call the ƒ I drew a “queer function”, but I wonder if a geometry like this isn’t more what queer theorists want than something as evanescent as “liminal”, something as thin as "boundary".

Transgressing boundaries, smashing binaries, and queering categories are important goals within certain schools of thought.

https://upload.wikimedia.org/wikipedia/commons/3/33/Anna_P.jpg

Reading such stuff the other week-end I noticed (a) a heap of geometrical metaphors and (b) limited geometrical vocabulary.

In my opinion functional analysis (as in, precision about mathematical functions—not practical deconstruction) points toward more appropriate geometries than just the [0,1] of fuzzy logic. If your goal is to escape “either/or” then I don’t think you’ve escaped very much if you just make room for an “in between”.

image

By contrast ℝ→ℝ functions (even continuous ones; even smooth ones!) can wiggle out of definitions you might naïvely try to impose on them. The space of functions naturally lends itself to different metrics that are appropriate for different purposes, rather than “one right answer”. And even trying to define a rational means of categorising things requires a lot—like, Terence Tao level—of hard thinking.

In harmonic analysis and PDE, one often wants to place a function ƒ:ℝᵈ→ℂ on some domain (let’s take a Euclidean space ℝᵈ for simplicity) in one or more function spaces in order to quantify its “size”….  [T]here is an entire zoo of function spaces one could consider, and it can be difficult at first to see how they are organised with respect to each other.  …  For function spaces X on Euclidean space, two such exponents are the regularity s of the space, and the integrability p of the space.  …  …        —Terence Tao  Hat tip: @AnalysisFact

I’ll illustrate my point with the arbitrary function ƒ pictured at the top of this post. Suppose that ƒ∈𝒞². So it does make sense to talk about whether ƒ′′≷0.

But in the case I drew above, ƒ′′≹0. In fact “most” 𝒞² functions on that same interval wouldn’t fully fit into either “concave" or "convex”.

So “fits the binary” is rarer than “doesn’t fit the binary”. The “borderlands” are bigger than the staked-out lands. And it would be very strange to even think about trying to shoehorn generic 𝒞² functions into

  • one type,
  • the other,
  • or “something in between”.

Beyond “false dichotomy”, ≶ in this space doesn’t even pass the scoff test. I wouldn’t want to call the ƒ I drew a “queer function”, but I wonder if a geometry like this isn’t more what queer theorists want than something as evanescent as “liminal”, something as thin as "boundary".


hi-res




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One of the more consequential kinds of extrapolation happens in the law.

In the case of Islamic law شريعة  the Hadith and the Qu’ran contain some examples of what’s right and wrong, but obviously don’t cover every case.

This leaves it up to jurist philosophers to figure out what’s G-d’s underlying message, from a sparse sample of data. If this sounds to you like Nyquist-Shannon sampling, you and I are on the same wavelength! (ha, ha)

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File:CriticalFrequencyAliasing.svg

File:AliasedSpectrum.png
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Of course the geometry of all moral quandaries is much more interesting than a regular lattice like the idealised sampling theorem.

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Lattice of beverages
Revised lattice



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imagering lattice
ring lattice

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Escher's grid







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Evenly-spaced samples mapping from a straight line to scalars could be figured out by these two famous geniuses, but the effort of interpreting the law has taken armies of (good to) great minds over centuries.

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A_2 lattice Voronoi and Delaunay cells
PCA of British MPs in the space of rollcalls

 

The example from this episode of In Our Time is the prohibition on grape wine:

  • What about date wine?
  • What about other grape products?
  • What about other alcoholic beverages?
  • What about coffee?
  • What about intoxicants that are not in liquid form?

The jurists face the big p, small N problem—many features to explain, less data than desirable to draw on.

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splines_2d_linear
splines_2d_cardinal
splines_2d_catmullrom
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splines_1d_cosineimage

Clearly the reason why cases A, B, or D are argued to connect to the known parameter from the Hadith matters quite a lot. Just like in common-law legal figuring, and just like the basis matters in functional data analysis. (Fits nicely how the “basis for your reasoning” and “basis of a function space” coincide in the same word!) .

Think about just two famous functional bases:

  1. Polynomials (think Taylor series),
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    and
  2. Sinusoidals (think Fourier series).
    Fourier Series
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Even polynomials look like a ‿or   ͡ ; odd polynomials look at wide range like a \ or / (you know how looks: a small kink in the centre ՜𝀱 but in broad distances like /), and sinusoidal functions look like ∿〜〜〜〜〜〜∿∿∿∿〰〰〰〰〰〰〰〰〰〰〰𝀨𝀨𝀨𝀨𝀨.

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So imagine I have observations for a few nearby points—say three near the origin. Maybe I could fit a /, or a 𝀱, a , or a ‿.

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All three might fit locally—so we could agree that

  • if grape wine is prohibited
  • and date wine is prohibited
  • and half-grape-half-date-wine is prohibited,
  • then it follows that so should be two-thirds-grape-one-third-date-wine prohibited—
  • but, we mightn’t agree whether rice wine, or beer, or qat, or all grape products, or fermented grape products that aren’t intoxicating, or grape trees, or trees that look like grape trees, and so on.

The basis-function story also matches how a seemingly unrelated datum (or argument) far away in the connected space could impinge on something close to your own concerns.

If I newly interpret some far-away datum and thereby prove that the basis functions are not  but 𝀨𝀱/, then that changes the basis function (changes the method of extrapolation) near where you are as well. Just so a change in hermeneutic reasoning or justification strategy could sweep through changes throughout the connected space of legal or moral quandaries.

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This has to be one of the oldest uses of logic and consistency—a bunch of people trying to puzzle out what a sacred text means, how its lessons should be applied to new questions, and applying lots of brainpower to “small data”. Of course disputes need to have rules of order and points of view need to be internally consistent, if the situation is a lot of fallible people trying to consensually interpret infallible source data. Yet hermeneutics predates Frege by millennia—so maybe Russell was wrong to say we presently owe our logical debt to him.

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In the law I could replace the mathematician’s “Let” or “Suppose” or “Consider”, with various legalistic reasons for taking the law at face value. Either it is Scripture and therefore infallible, or it has been agreed by some other process such as parliamentary, and isn’t to be questioned during this phase of the discussion. To me this sounds exactly like the hypothetico-deductive method that’s usually attributed to scientific logic. According to Einstein, the hypothetico-deductive method was Euclid’s “killer app” that opened the door to eventual mathematical and technological progress. If jurisprudence shares this feature and the two are analogous like I am suggesting, that’s another blow against the popular science/religion divide, wherein the former earns all of the logic, technology, and progress, and the latter gets superstition and Dark Ages.

(Source: BBC)




@jtc_19 asked:

The isomorphismes links (last three tweets) might be worth sharing with everyone. (I’ve been accused that this site is hard to browse—sorry!)

@isomorphisms haha, yep.

— Clark (@jtc_19) April 15, 2013

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By the way! OCW has course notes on the standard weird phenomena and also the standard interpretation of the physics. http://ocw.mit.edu/courses/linguistics-and-philosophy/24-111-philosophy-of-quantum-mechanics-spring-2005/lecture-notes/




I’m bored of #ff meaning follow Fridays. Let’s do Failure Friday instead and talk about things we’e failed at.

  • I failed an arithmetic test.
  • I failed judo class.
  • I failed to attract interest with my CV.
  • I failed to be married or have a stable job by my 30th birthday.
  • I failed an entrance exam.
  • I failed most of my writing assignments.
  • I lost an important contest.
  • I lost a race. Badly.
  • I lost a client I thought I had secured.
  • I failed a client I thought I could help.
  • I failed to get paid what I thought I was worth.
  • I failed to be honest in a romantic relationship.
  • I failed to do anything cool for a few years.
  • I couldn’t walk on a mountain because I was so out of shape.
  • I failed to wear sunscreen.
  • I failed to read the prospectus.
  • I failed to get into my preferred university.
  • I failed to get someone to fall for me.
  • I didn’t know what I wanted or how to get it.
  • I failed to keep in touch with old friends.
  • I failed to impress people.
  • I failed to advocate for myself.
  • I failed to do things on time.
  • I lost Other People’s Money.
  • I failed to come up with good ideas.
  • I failed to give it my all.
  • I failed to lose weight.
  • I failed to meet expectations.
  • I failed to look “put together”.
  • I failed to stay organised.
  • I failed to Get Things Done.
  • I failed to cook a good dinner.
  • I failed to recognise the obvious signs.
  • I failed to learn what I was trying to learn.
  • Things did not go according to plan.

NB: I don’t intend Failure Friday as a pity party. It just bugs me when people try to act flawless and successful. Infinitely wise with inerrant self-command. Even apparent failures are successes in disguise. Sorry stories modulate into major key as the lessons learned were invaluable rungs on the ladder of upward progress so in the end it all worked out for the best.

What is that? You’ll probably just make people who are already down feel worse by doing that. And not make anyone feel better.




This was a rhetorical question our chess teacher used to ask us. It’s a reminder that even though materiel, position, and tempo are worthwhile achievements that advance your interests, the goal is to check-mate the King.

For example the Blitzkrieg or “Scholar’s Mate” doesn’t capture materiel or obtain an advantageous position. It just goes directly for the kill.

It’s worth asking this question whether you’re just out the gate or mid-game. Is there a way within a few moves that you could mate early? Never forget to look for that in the quest for materiel or position.

  

I use the question now in my life as a shorthand for

  • why am I doing this?

. Getting money, obeying authority, learning things, obtaining credentials (résumé builders”), maintaining a low weight—all are “good” goals which advance my interests. But why? What is it aiming towards? What am I really trying to do?

In chess the goal is well-defined, whereas in life one can choose one’s own goals. In particular they can be

  • continual (“Go for walks”)
  • or circular (“Raise kids, so they can raise kids, so they can raise kids, …”)
  • rather than once-and-done (“Get thin”, “Mate the King”).
  • (And they needn’t be zero-sum.)

I think that makes the question What is the object of the game of chess? even more important.

That’s something that helps me and I hope it helps you. I’m going to pause now for some quiet reflection.