Probability of finding a four-leaf clover

Short answer: around 1 in 2,000.

(Clarification: this is the probability that, if you pick up a single leaf at random, it will have four leaflets.)

Here is my collection of four four-leaf clovers (out of five, the fifth has shredded leaves), collected over a period of two weeks.

If you look at the wikipedia page (& refs therein), the most commonly cited figure is 1 in 10,000. Unfortunately there are no actual observations reported anywhere.

But now I can report that, according to my very empirical research, the probability of finding a four-leaf clover is probably more like 1 in 2,000.

How do I know?

1. I find that I can scan around 100 plants per minute.
2. Most recently, I found two four-leafs in about 30min worth of scanning.
3. This gives a rate of 1 in 1,500

The previous attempts have however been slightly longer, although I didn't time them as accurately. Also, the actual number of plants scanned per minute can vary due to wandering attention. So, I would think a more conservative estimate is ~1 in 2,000.

Of course, these are all in upstate NY, although not at a single location. Perhaps these rates vary with a whole bunch of other factors.

Still, these are fairly low odds - finding 5 four-leaf clovers, even with these better estimates, is still less than one in 10 quadrillion! (Clarification again: this is the probability that, if you pick five leafs blindly, all five will have four leaflets each.)

Innovations: Segway to language

A signboard on my way home: "High-tech gadgets repaired."

What really is a high-tech gadget anyhow? Take the Segway. Nothing like it existed before it did. It would be hard to argue that this was not a genuine innovation - and a reasonably high-tech one.

But what makes it high-tech and an innovation at all? Certainly, as this gentleman shows, it isn't stuff like the "brushless servo motors with neodymium magnets" or wheels of "sophisticated engineering-grade thermoplastic."

That is, all the parts pre-existed, and can be replaced by equivalent, crappier parts that in themselves are old hat, and aren't necessary for the innovation itself.

What about the software? Well, it's using some version of C or Python or some such. So that's not new. Neither is the general problem, which as Wikipedia tells me, is that of the inverted pendulum.

So why is the Segway an innovation? And really, is it even an innovation at all? I think you might agree that, in a sense it is. Oh sure, maybe someone else thought of the idea before and never got around to implementing it, but as far we know, Dean Kamen invented the Segway.

Now here's the point - I think it's the same deal with language and cognition. Sure, language might rely on a whole bunch of stuff - the cognitive equivalent of neodymium magnets and thermoplastics, but in the end, I believe that it is a genuine innovation like the Segway is.

Look at what the Segway relies on (/is made up of), and you find that all the pieces pre-exist, and can be found in several other, crappier devices that don't do half as much. Look at the code, and you'll find data structures and operators from the simplest "Hello World" program. Similarly, look at what language relies on (/is made up of), and you'll find the same old cognitive systems like memory and attention and, I wouldn't be surprised, sex, drugs & rock'n'roll; cos those are the bits the mind is made up of anyway.

But nevertheless, like the Segway is an invention of Dean Kamen, language is an innovation of our species. So the next time you read a paper that pretends that language is nothing more than memory or attention, think of the Segway.

Worst article ever. Or, who has seen the wind?

Finally the special issue is out, and it looks like balance, intelligence, a broad biological perspective and just plain good reading habits lose to rhetoric, misrepresentation and... and I really do not know what.

The culprit, which I think is possibly one of the worst articles is by Spencer et al, and is the first in a special section: Is It Time to Look Beyond the Nativist–Empiricist Debate? in the August issue (Vol. 3,No. 2) of Child Development Perspectives.

The point of the paper is hard to understand, given that, I think, most nativists would have no problems with most or any of the examples they give. Why the fact that development "emerges via cascades of interactions across multiple levels of causation, from genes to environments" should pose a problem for the innateness thesis I cannot fathom. Of course, the adult biological entity is a product of genes and environments. How one can possibly have any kind of theory involving, e.g., nouns and verbs that is derived from such an understanding of development is presumably left as an exercise for the reader.

Everything, language, cognition - must be grounded in theories of development, in their view. It reminds me of the poem by Christina Rossetti:

Who has seen the wind? Neither I nor you. But when the leaves hang trembling, The wind is passing through. Who has seen the wind? Neither you nor I. But when the trees bow down their heads, The wind is passing by.

The point is, and this is probably not the best way to make the point, that "wind" is not really something you can see, just as "language" is not something you can see. You call the (generative) force that hurries leaves along "wind", just as you call the mechanism that drives words from your lips "language". Grounded, whether in the sense of Spencer et al, or grounded in the sense of embodied cognition, I find it these conflations of various interlocking questions: what is a good theory of the generative systems (the langue) that propel the various specific instances, heard and unheard (the parole)? How does this come to be? In ontogeny? In phylogeny?

It seems to me that there is one main reason for writing this paper- the various 'critics' seem to think that, if something is identified as "innate", then research stops. Perhaps so, but that depends entirely on the level at which one is researching. If I am studying comparative behavior, then I might be content to report that:

(1) Chickadees can be tamed in adulthood, while almost no other passerine can.

Does this come out of a "complex interaction of genes and environment?" Undoubtedly?! But does it make a statement like (1) something no researcher should abide by? Well, not for me.

Will the elaborate and "inconvenient" (in their case meaning [1] complex or [2] amenable to much broader range of phenotypes than those the typical environments allow) developmental research shed any immediate light on, e.g., why we can understand and explain to someone the rules of chess? Personally, I'd put that question on par with a quantum theory of tectonic plate movements.

Maybe it's a lack of exposure to Fry & Laurie at some critical stage ;)

Backup systems on spaceships

Watching old Star Trek: Next Generation. In this episode (Disaster) the Enterprise collides with a quantum filament (whatever that might be), and things aren't very spiffy anymore aboard the vessel. Life support systems are compromised and the field holding the ship together is packing up for a little vacation.

Anyhow, that got me thinking - if I were to have any say in the design of a spaceship, I think that besides the various backup systems, fault tolerance, hierarchical, modular structures and self-healing material, to also make sure that for each critical system, there was at least one backup with a totally different technology. So, for e.g., if a quantum filament hits you and quantum systems are jinxed, you can switch over to a classical system. The fundamental idea being that the cause of the damaging element would be unlikely to affect two technologies that were fundamentally differently implemented.

Which nicely brings us back to Marr and his levels :)  To restate: the spaceship would benefit if the systems for each critical function (the computational level) was implemented (implementational level) in two distinct ways, so that if something caused a failure of the implementational bits of one system, it would be unlikely to also affect the implementational bits of the second system. 

 

Featured!

I got featured in the Observer magazine of the Association for Psychological Science!

Also, I realized I haven't really been blogging in a while. Which is not to say there hasn't been anything interesting :)

iPhone!!

Since it's not yet possible to jack into the matrix, at least there's the iPhone :)

Mobile Blogging from here.

[Posted with iBlogger from my iPhone]

The plan

Me and Katherine are working on an anticipatory looking paradigm, and we've designed a system for creating and analyzing Tobii experiments. Starting from this system-level design, Johnny Wen has written a most marvelous MATLAB project. It's amazing how far this cluttered-looking whiteboard has come :)