My Math Forum Question on exponential functions

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July 20th, 2017, 05:25 PM   #11
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 Originally Posted by skipjack That's fine; however, the "official" line of many faiths is that you can't have a personal view that conflicts with any of various key tenets of the faith. If they didn't have such a line, it would make it meaningless for you to say that you adhere to such a faith, as most people wouldn't know your personal view and hence wouldn't understand what your adherence meant. Also, of course, the personal views of most people change from time to time on at least some issues, so whatever you currently think is right you might consider to be wrong a bit later.
Which is why I'm not a devout anything in the religious arena.

However from what I know (and can remember) of the bible, I don't recall anything in it that would be contradictory to science...unless you take every word in it literally. I had a coworker some years ago when I was in the Air Force, heck of a nice guy, but he believed the earth and the heavens were created literally in 7 days. He also was one of those "the earth is only 6000 years old" types too, soooo

Of course, my views (and to a great extent my knowledge) is limited to that of a white male raised in the southern U.S.

I've been pretty steadfast in how I view the relationship of science and religion most of my life (it did take a while to grow, become educated and gain some worldly experience). I don't if I will ever change it, but anything is possible!

July 20th, 2017, 05:33 PM   #12
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 Originally Posted by Micrm@ss The existence of God has nothing to do with creationism really. In the sense that one can believe in God and also accept the theory of evolution. The theory of evolution is an established scientific fact. So creationism is provably wrong, unless you're going to jump through an amazing amount of weird hoops. The existence of God is not at all affected by the theory of evolution. See for example the Catholic church which accepted the theory of evolution as truth many years ago.
Agreed, and that very subject is why I think so many people have misinterpreted the bible, or at the very least they take the words too literally.

Genesis, for example, tells us that God created the heavens and the earth and he put us on it. That's fine, and I don't debate that. Evolution, to me, is just the mechanism to that end. I think some people think he literally snapped his fingers and POOF, here we are. Given that evolution is proven, and in conjunction with so many other things we've learned and understand now, it makes sense that it took quite a while before mankind (as we generally accept the definition today) showed up. God did whatever he did to put these things into motion and eventually, here we are. There's no difference, he still "made us."

July 20th, 2017, 05:46 PM   #13
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 Originally Posted by EDL Agreed, and that very subject is why I think so many people have misinterpreted the bible, or at the very least they take the words too literally. Genesis, for example, tells us that God created the heavens and the earth and he put us on it. That's fine, and I don't debate that. Evolution, to me, is just the mechanism to that end. I think some people think he literally snapped his fingers and POOF, here we are. Given that evolution is proven, and in conjunction with so many other things we've learned and understand now, it makes sense that it took quite a while before mankind (as we generally accept the definition today) showed up. God did whatever he did to put these things into motion and eventually, here we are. There's no difference, he still "made us."
Sure, this is called Theistic evolution. And it is also where science and religion separate. Science cannot say more about the existence or non-existence of god. Religion cannot say more about the natural world we observe. They are both perfectly compatible since they talk about different areas.

July 20th, 2017, 07:14 PM   #14
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 Originally Posted by EDL However from what I know (and can remember) of the bible, I don't recall anything in it that would be contradictory to science...unless you take every word in it literally.
This is exactly the problem. What is to be taken literally, and what is not.

If you wish to take 'advice' or moral value from the bible and then cherry pick what you think is to be taken literally or not, then why bother at all?

July 21st, 2017, 02:21 AM   #15
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 Originally Posted by EDL Our instructor is always urging us to think about the math and not just plug numbers into a formula and spit out answers, ...
Great!

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 If I were to plot a basic exponential that illustrates the growth rate of computing power over time, let's say $\displaystyle y=3^x$, then the x axis is the time line (and asymptote) and the y axis is the power of computers. Since x is an asymptote, then no matter which year I pick, y will always have a positive value. How can this be? If look at a point in time 300 years ago, I get a positive value, even when computers didn't even exist. There is obviously a flaw in my understanding, or there is something else to this that I don't know. I'm guessing both. What am I missing?
As people have said already, you're just missing the fact that mathematical models of things are applicable to particular conditions or domains. For the case of Moore's law, it applies well to things like transistor density or processor speed (not all things...) and only for certain periods of time. Since manufacturing processes for particular items of computer hardware are approaching the atomic scale (~ nm) there are fundamental barriers to existing trends and it's interesting to read about the possible technological achievements that could ensure that Moore's law continues or how it changes as a consequence.

Every mathematical model has conditions or domains of applicability. They also have a set of assumptions that are inherent in the building of the model which outline how the model behaves under those conditions within the specified domain. If the model can be compared to another scenario or situation that is more detailed (e.g. reality) then the model will probably only approximate the situation or scenario and the model can be considered a success if the error is low enough to satisfy whoever's using the model.

Laws of physics are no exception. Newton's laws, for example, only work when the velocity of the objects involved are low; when those objects start travelling faster and faster (closer to the speed of light), the error found when comparing the calculations to reality is so large that Newton's laws simply give incorrect answers and can't be used anymore. Therefore, when using Newton's laws to solve a scenario involving every day objects, there is the assumption that relativistic effects caused by rapidly moving objects are ignored. Being aware of these kinds of assumptions or conditions is important when doing any mathematical modelling.

Also, as suggested already, there are two ways of predicting something new, interpolation and extrapolation. Interpolation is predicting something by considering a middle ground between two points, whereas extrapolation is going beyond a point into unknown territory. In general, extrapolation is considered more dangerous because you're effectively widening the domain of applicability that you assume your model is valid for. However, it really boils down to how well the trends are understood. There are a rare few phenomena that can occur where orders of magnitude changes in a particular trend are observed for tiny changes in a variable that may have been missed in a broad-brush study (such as nuclear resonances). In such situations, interpolation is just as dangerous as extrapolation. Thankfully, such situations are very rare, so 'surprise!' instances don't happen very often and we can still predict things.

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