Greylorn Ell wrote:...
I'm willing to give this another go, but beforehand I need to know your mathematical background. Have you taken a university-level course in probability theory? If so was it geared for biologists, mathematicians, or physicists? I ask this because it seems as though you do not understand what I've written on this subject, and I need to know your level of education before generating an explanation that you might understand. ...
My mathematical abilities are abysmal, so go for the really simple explanation please.
I appreciate your honesty. I'd like to try something that might benefit both of us, and which might also be of value to anyone reading but not participating in this thread. It will require your cooperation and your curiosity. I propose to teach you the basic principles of probability mathematics, and show how they apply to genetic mutations. Specifically, I'll show you the math behind my calculation, if you are willing to learn it. First a few comments that relate to your style of thinking, as I perceive it to be.
People who are not hard scientists have a tendency to trust science-authority figures. If unable to follow the mathematical logic, they have no other choice. Some of those with a hard science background suffer the same problem, but at a higher level. A physics student might find Newton's Principia Mathematica
fairly easy reading, yet be dumbfounded by Feynman's Theory of Quantum Electrodynamics.
My personal theory of human understanding claims that hardly anyone really understands deep theory, and that is why experiments are so important. For example, every student graduating with a B.S. in physics must know Relativity Theory and basic electrodynamics. Suppose that those post-grads who wanted to go on to graduate school were evaluated not by their accumulated grades, but by a simple two-hour snap quiz (unanticipated, so not studied for the previous night) that included one of these questions:
Using the data, physics knowledge, and mathematical tools available to Maxwell at the time, derive
his four equations of electrodynamics from scratch.
Using the same kinds of tools as available to Einstein, derive
his Theory of Special Relativity.
Such fundamental-level entrance exams are unlikely to be given, because doing so will quickly deplete physics graduate schools of students, thus depriving worthless teaching professors of a useful function, and perhaps eventually an income.
I mention this only to point out that at some level, everyone in science must accept the authority of previous work. I could not pass the test just outlined. No course I've ever taken required students to solve such a fundamental problem. I've tried understanding those derivations on my own, but failed. The best I (and perhaps many others) could do was to apply their results.
You, like other non-scientists (non-physicists, anyway) are pretty much stuck believing in authority figures, just like churchgoers believe in their scriptures and religious leaders. This shows in your comments, where you reference the beliefs of selected Darwinists, for example. This trust in authority on both of our parts works out fine for the most part-- but fails when the authorities are incorrect.
I've learned the long way that arguing with someone who quotes his authority figures is a complete waste of time. The best I can do is to trot out authority figures of my own. Our conversation about the mathematical soundness of Darwinism would soon degenerate into an action-figure game between two children. Let's not do that. I would prefer to show you how to become your own authority figure. The way to accomplish that is for you to learn basic probability math.
Of course you might wonder if I have the skills to teach you properly. The wonderful thing about math is that there is no other way to teach it. Its logic is internal. The only thing that I can do is to teach you how to recognize and use that logic. When you get the logic, you get the math. It is independent of whoever explains it.
If you are interested in this project, let me know. It would be discourteous of me to proceed otherwise.
Greylorn Ell wrote:Then, consider the value of playing a simple game at the cost of 35 pounds (or dollars, your choice) per play. If you win you'll get 100 pounds back.
3 green marbles and 2 red marbles are placed in an opaque bag. You must reach into the bag blindfolded and pick one marble, put it on a table. Then, same thing. You win if you end up with two green marbles on the table.
Suppose that you are allowed to play this game 1000 times, allowing the odds to average out. At the end of the 1000 plays, will you be richer or poorer? And for the big prize, by how much?
It would be best if you can answer this little problem without recourse to a consultant or adviser. Should you want to do a bit of research into basic probability math before answering, you will learn something from the experience.
Thanks for the exercise. I'll use it to teach myself the basics but since this'll take a fairly long time given my starting point I'd appreciate it if you could address my question below in as simple a manner as you can.
It need not take you longer than this weekend-- or the next if you persist in dragging your feet. And I'll do better than answer that question. I'll show you how to answer it for yourself.
Greylorn Ell wrote:Sorry, but I missed this, and will review/answer it if I can find it. Can you give me thread name, page number, and posting date? Thanks.
No need as we can use your example just as well. So take your marble-game, what would happen to the futures results if when I win with two greens one of the reds turns green? I.e. a kind of natural selection is implemented with respect to the probabilities of green marbles occurring in future.
Because those who see physics from the perspective of a documentary-channel viewer are regularly exposed to blackboards or windows filled with irrelevant esoteric equations that are never explained in context, people do not appreciate the importance of simplicity in math and physics. The complex equations you see on TV serve only one purpose-- that of intimidating the viewer into thinking that he can never understand that gobbledegook on his own, and must trust the authority figures on his screen. That's utter bullshit. Basic physics involves simple principles expressed in simple mathematical formulas.
This simplicity is arrived at by reducing physics to simple examples, then keeping them simple until the problem is resolved. For example, Newton's 2nd Law of Motion was experimentally derived by Galileo, by timing wooden balls rolling down inclined planes with a simple water-clock.
Your question is an immediate attempt to complexify a simple problem. It is better answered in the context of quantum mechanics, and we are not ready for that yet.
There is another factor to be considered, which is, does a particular mathematical problem actually apply to a physics or biology question? We will be better equipped to resolve that question after you have learned to solve some simple mathematical problems.
If you wish to proceed, here are the basic standards of probability math.
Probabilities are measured within the scale of zero to one. Zero means, cannot happen. One-- must happen. 0.5 means, even shot.
Sometimes people like to express probabilities in terms of percentages. This is managed simply by multiplying the value by 100. Thus, 100% means that it must happen, and 50% means even chance.
Your first exercise is, given the above example, what is the probability of pulling one green marble from the bag of 3 green, 2 red marbles? Use common sense to solve the problem, then express your solution as a number in the range of 0-1, or as a percentage.
Then, from the same initial conditions, what is the probability of pulling one red marble?
Greylorn Ell wrote:My answer will depend upon your reply to this post, of course. There's no point in replying otherwise, as I'm sure you'll understand.
I thought you said that your reply depends upon what level my understand is, not that you wouldn't be replying. My understanding and experience of those who know what they are talking about is that they can explain it in simple terms if necessary.
If your reply showed that you could not or would not do some work on your own, I'd be wasting my time.
You and I share similar understandings of explainers. However, whether or not something can be explained depends upon the recipient's intelligence and prior knowledge. A normal 7-year old cannot be taught calculus, nor can a bright college philosophy student who does not know algebra and trigonometry. I am as certain that the Queen of England cannot learn calculus as I am that Obama cannot learn anything of consequence.
This conversation arose because you were asking good questions but clearly were unable to make sense of my simple answers. I'd like to answer your questions is such a manner that you completely understand my answer. You will need to understand basic, simple, probability math first. Most importantly, you
must own whatever understanding you acquire. I'll work with you, but if you bring B into the conversation, I'm gone. I have better things to do than engage in further conversation with any truculent jackass who pretends to expertise that he does not manifest, and who invents his own "facts."
I cannot stop a jackass from braying, but if you feed him, you own him, and I'll assume that you lack the courage to obtain your own understanding, and will be forever dependent upon authority figures with dubious authority. If that's the case, I'll leave the two of you to your own devices, forever, with some small regrets in your instance.