Toothpaste isn’t made from ground teeth.

# Mind Blowing Facts

**glia**#186

made me think of this

which proposes a “fact” about arachnid webbing being part of their cognition processes

if true…

it would blow my mind to know that webs can function as an extension of their brain

**TangoWhiskeyman**#187

Writing is an extension of the human brain, isn’t it? And from that, maps, and computers, and so on…

**glia**#188

well that’s what i find so fascinating about the prospect

i need to re-read the findings (and search for more recent developments) but from what i gathered before…the web seems to go beyond capabilities of a relatively simple tool like a map

if not actually part of their brain

a web seems closer to a complex machine/computer (for them) when you think about the kind of two-way feedback produced

**bjarlstedt**#190

”Black panther — a term that can be used for any black big cat, but in Africa is usually applied to a black leopard.”

Had no idea.

**ht73**#192

I think this is pretty much for every living thing, including humans. that’s why the devastation of the environment is an assault on consciousness. but the assault of course began long before, with the notion that consciousness is this reified thing inside the human brain, or that it is even “ours” to begin with. the assault is what made the devastation possible, in other words.

A good neuroscience-oriented primer on all this is Alva Noë’s *Out of our Heads*. It’s a quick read and not as technical as some of his other books.

Noë’s is not my favorite perspective on this matter, as he’s almost completely devoted to the science, but it should then be especially convincing to those with the typical American scientific/cognitive psych/analytic philosophy background; i.e. the people who most often unthinkingly promulgate the notion that consciousness is a reified thing inside the head. I think Noë wrote it more as a way to expose how contemporary neuroscience is overturning its own.founding presuppositions.

**ht73**#193

In Zermelo–Fraenkel (ZF) set theory, the natural numbers are defined recursively by letting 0 = {} be the empty set and

n+ 1 =n∪ {n} for eachn. In this wayn= {0, 1, …,n− 1} for each natural numbern. The first few numbers defined this way are:The set

Nof natural numbers is defined in this system as the smallest set containing 0 and closed under the successor functionSdefined byS(n)=n∪ {n}. The structure ⟨N,0,S⟩ is a model of the Peano axioms. The existence of the setNfollows from the axiom of infinity in ZF set theory.

**alanza**#194

I happened to read a short paper/essay by a mathematician who cares deeply about this kind of thing (I don’t, particularly), who argued that the belief that repeatedly exponentiating a natural number gives you a natural number is “just that, a belief”. More broadly he took issue with the successor function, arguing, I think, that a “completed” infinity—that is, an infinite object that you can somehow study all at once rather than viewing it as a process or as something that continues—is a concept we should be concerned about.

In that vein, some people studying the foundations of mathematics consider very large (i.e. massively, wildly infinite) cardinal numbers and have amusing names for them:

**ht73**#195

Interesting… I think you get this kind of indescribability already with the Ackermann function, which in the general case can only even be *written* in terms of itself, it’s kind of an object without any sense, one that can *only* be approached through formal properties. Descartes would have loved it. Anyway I’ll have to think some more about shrewdness. Transfinite stuff in general already boggles my mind

**alanza**#196

My only connection to the Ackermann function is this very cute idea of Hercules vs the hydra, which I know of via its occurrence within group theory, but this article seems like a nice explanation of the idea.

**csboling**#197

I find myself sympathetic to but not terribly passionate about a position, related to intuitionistic logic, that I’m probably mischaracterizing as “a proof needs to be computable to be sensible - a proof is a program, and that program had better terminate, preferably in polynomial time”.

**ht73**#198

More depressing than mind-blowing …

(the US pet tiger population is almost double the **world** wild tiger population…)

**alanza**#199

Decided I’d post here rather than Joy in Pictures.

I’ve never watched *It’s My Turn* (I’m told it’s not a good romcom), but I do love that this scene gives a totally correct proof of the Snake Lemma. Given Hollywood and that relatively few people would have noticed had the math been wrong, I suppose that squeaks in as mind-blowing.

Since we are, in fact, “addressing ourselves to the cohomology of groups” on Monday and hopefully on-and-off thereafter I decided I wanted a set of notes to refer back to when I get rusty, so I made one. Mostly I wanted an excuse to show off how pretty the diagram is xD