Category Archives: science

I Am, Therefore I Think

Consciousness is one of those nebulous concepts, at least in the ‘normal’ non-academic world. Some say there is no such thing, a delusion. It’s just how the body refers to itself and organizes its sensory processing. There are so many theories. On the other side there are the religious, spiritual views that posit that there is something more then the meat body, more then just electro-chemical discharges. In between there are some investigators finding that the traditional views are lacking. Some even claim that consciousness derives from deep quantum mechanical processes; quantum effects are relevant at room temperature and macro scales.

Heck if I have an answer. I just Am.

I’ll make one observation though. Seems that people argue about consciousness from the mental processing angle. That is, if something is conscious it exhibits certain properties. Yet, stop the flow of thoughts and what remains is awareness. How can awareness be awareness of being aware? Or is it just the body all along that encases the waking state dream?

  1. Cytoskeletal Signaling: Is Memory Encoded in Microtubule Lattices by CaMKII Phosphorylation?
  2. Consciousness
  3. OnLine Papers on consciousness
  4. Consciousness; Internet Encyclopedia of Philosophy
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Science brain hype?

Is science any closer to understanding the most complex object in the universe, the human brain?

Nope. In fact not only is the hard problem of human consciousness still a problem, even little things are, like visual cognition. Well, I’m not an expert, but that’s the idea you get from being a consumer of science.

Just the other day I was reading about an astounding science experiment. Would you believe, a neuron in the brain can be used for more then one task. Wow! That is like so 1940’s. Next there will be a discovery of artificial neural networks (ANN). Perhaps, its how these press releases are created and how they have to be dummed down for publishing that gives the impression they are just going over old known facts.

Here is an idea for a ground breaking science project. Why does my cat move? I mean she was fed and that part of the floor is just like that other spot on the floor. Where did that impulse come from? I mean really from? Or is it all part of a cosmic quantum flotsam of macro-predictability in some multiverse of 108 dimensional karma that demands that my cat at this precise pico-second will move from that spot on the rug to that other spot?

Ok, Science, until you can answer that, leave my brain alone.

P.S. 7-23-12: Wow, I wrote this as a quick reaction to something I was reading. Now today doing a web search I found a very relevant article: Is Brain Science Just Hype?

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Are lottery odds incorrect, and your chances drastically worse?

A simple application of elementary probability shows that lottery odds as reported by the operators are incorrect.

Note: I have delayed posting this for a while since the results I come up with seem incorrect. Hopefully someone can respond and tell me where the problem lies.

About a year ago while speaking with my brother Robert on the phone he casually mentioned a joke he made. He said lotteries are so funny since you have to pick the winning number twice in order to win. We both laughed.

But, then later I did a double take, huh? That is true, you have to pick the number set, and then a few days later, the lottery company will also pick a set. If the sets match then you win. Ok, that makes sense. But, if seen this way, the probability value they give for winning couldn’t be correct. Could it? They only give the odds of picking any set, not the winning set. It has to be much harder to win, thus, the probability much lower.

How to compute the Probability?
In probability theory there are rules for combination of events. If the events in an “experiment” are independent, you just multiply the probability values of each: P(A and B) = P(A intersection B) = P(A)P(B).

Further details are on this High School wiki page:

Multiplying probabilities

Probabilities are multiplied together whenever an event occurs in multiple “stages” or “steps.” For example, consider rolling a single die twice; the probability of rolling a 6 both times is calculated by multiplying the probabilities for the individual steps involved. Intuitively, the first step is simply the first roll, and the second step is the second roll. Therefore, the final probability for rolling a 6 twice is as follows:

P(rolling a 6 twice) = P(rolling a 6 the first time) X P(rolling a 6 the second time) = 1/6 X 1/6 = 1/36 approx 2.8%

Similarly, note that the multiplication of probabilities is often associated with the use of the word “and” — whenever we say that some event E is equivalent to all of the events X, Y, and Z occurring, we use multiplication to combine their probabilities (if they are independent).

More info on this wikipedia entry: Probability, Mathematical treatment

Does this apply to the lotteries, like Powerball? There are two events, though separated by days. The consumer, player, picks a set, then later the operator picks there own set. And, they are independent, neither event is dependent on the other. So, the problem, to me, is interpreting the “experiment”. I contend that the whole game, which takes place over a few days is one thing, an experiment, and so the multiplication rule applies.

Another way of relating them is to use two die rolls. But now instead of a die with six faces we use N faces, where N is the total number of possible number sets we could pick in a lottery game. This “die” is really a form of Spherical polyhedron. Lets say N is 195,249,054 possible unique numbers, which correspond to each possible set. So when we roll two dice the total probability would be (1/195,249,054 X 1/195,249,054). Remember, these are “normal” die, just having a ginormous number of faces.

The above is not even mentioned in the Lottery math references, for example, this Wikipedia entry, Lottery mathematics. So some conceptual misunderstanding on my part is very likely.

Example
Lets take an actual example, the Powerball lottery states on their “Powerball – Prizes and Odds” page that to win the Grand Prize the odds are: 1 in 195,249,054. This is derived by application of math stuff to determine the combinations of the five white balls (1-59) and a red ball (1-39).

If we apply the multiplication rule the actual probability of winning is:

1 in 38,122,193,087,894,916

That’s 1 in 38 quadrillion. Big difference!
In scientific notation: 3.8122193087894916 x 1016

What is the Expected Value now?

Error?
This analysis couldn’t be correct. First, the number is too large, there are too many winners. Second, I have never heard of anything like this. Surely if this were the case it would be news. So where is the mistake?

I think it has something to do with the “same set of numbers”. Then its not just a simple multiplication of probability? If I find out, I’ll update this post.

So what?
You should not be paying the “idiot tax”. True, but when the prize reaches 100 million I bet there are some math professors out there buying a ticket too. Further, it is an interesting math subject.

Updates
This article analyzes the occurrence of a lottery draw that duplicated the same numbers and argues that my kind of instinctive analysis above is incorrect. Adventures in Probability. So, perhaps, the way to look at this issue is to compute the probability of the same winning combination being picked twice in a row? What the article says that it is 3.8 X10^16 but this has to be multiplied by the amount of combinations, so:
(1/((3.8 x 10^16) * 195,249,054))*195249054 = 1/195249054. That same as what the lottery provider quotes! I don’t get it yet. Then why are the two dice example not calculated in the same way?

Further Reading

Off Topic

Appendix
Groovy program to print the product:

x = new Long('195249054');
printf('%,d',(x * x));
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Eye of Odin

My Ubuntu’s (in my Virtualbox VM) background image cycles thru some great galactic images. But, now when this one comes up all I see is a left eye. The resolution and color depth heightens the affect; on my screen I even see the outline of a nose on the right.

The Helix Nebula: a Gaseous Envelope Expelled By a Dying Star
Source: Hubblesite.org

Anyway, be a good person. Your being watched! 🙂

The image is of: The Helix Nebula: a Gaseous Envelope Expelled By a Dying Star

Links
Hubble

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