Exponential Digits

[cheesehead]

Originally Posted by ndpowell

OK! I am lost on the terms "floor" and "ceiling" beyond their obvious meanings.

Let MathWorld (at http://mathworld.wolfram.com/ ) be your friend. Go to the Alphabetical Index at http://mathworld.wolfram.com/letters/ and proceed from there for just about any math term you might encounter.

[R.D. Silverman]

Originally Posted by drew

Hey R.D. Silverman,

This seems *very* condescending. You have to understand that most people left high school behind and pursued careers that had nothing to do with math, or at least not enough to care about logarithms (as useful as they are). I'd bet most people didn't remember these logarithmic identities more than a couple of months past that particular chapter in algebra class.

In fact, I remember an instance when I was in high school where one of the math teachers asked me to show her how to compute logs with an arbitrary base, because she didn't remember (it's not something she normally taught).

I understand you have a PhD, and you appear to be an expert in math. Understand that this means you know a *lot* more than the average Joe about these things. No need to make them feel inadequate because they happen to have enough interest to dabble a bit in your field of expertise as a hobby. They should be encouraged, not criticized.

Drew

Ah yes. The "dumbing down of America" is OK point of view.

I will refer to U.S. citizens. Those not native English speakers or not
U.S. citizens may adjust my comments and questions accordingly.

(1) Knowledge of logarithms is basic level mathematics. Anyone without this
knowledge has no business participating here.

I have a good knowledge of mathematics. I love the ideas behind string
theory and quantum gauge theory. However, I do not presume to "dabble"
in these areas because I recognize that I lack the REQUIRED SKILLS. My
knowledge of differential geometry and differential topology and algebraic topology is quite weak.
I have no business "dabbling" until I acquire the needed skills.

(2) Allow me to paraphrase Robert A. Heinlein
"Anyone who can not cope with mathematics is not fully human. At best
they can be trusted not to make messes in the house"

(3) A U.S. High School Graduate should be able to

- discuss the difference between a plant and animal cell
- define 'dangling participle', 'faulty parallel sentence structure'
- be able to conjugate the verb 'to be' in whatever foreign language they
studied. And if they did not study one, shame on them.
- describe the difference between column 1 and column 7 of the periodic table
- describe the 9th and 10th amendments to the U.S. Constitution. Explain the
dispute Andrew Jackson has with the U.S. Supreme Court
- define 'centripetal force'
- be able to calculate with logarithms; be able to solve a quadratic equation
- name 3 19th century U.S. presidents other than Lincoln
- name 5 U.S. authors of the 19th century and describe the contents of some
of their books (as well as titles)
- Identify Madagascar on a map. Name the capitol of 20 countries other than
the U.S.

etc. etc. etc

Unfortunately, most adult Americans are, IMO, ignorant fools who should
not be given the right to vote. Saying "I studied this way back in high school" is not an acceptable excuse. I still remember most things I studied 30 years
ago.

I admit that I am an elitist snob. I personally believe that ignorance should
not be tolerated. I demand excellence in myself in what I do and expect the
same of others. If something is worth doing, then it is worth doing WELL.

They may not *care* about logarithms, but they should remember how to use
them. If we all only remembered the things we care about, then the world
would be totally filled with ignorant fools instead of being 90%+ filled.

And if a person cares enough about this subject to enter into discussion
groups then they should care enough to acquire the necessary background.

If a person can't remember what they learned in high school then they *should* feel inadequate.

[xilman]

Originally Posted by R.D. Silverman

(3) A U.S. High School Graduate should be able to


- Identify Madagascar on a map. Name the capitol of 20 countries other than
the U.S.

- Know the difference between "capital" and "capitol" and when to use each of them.

Remember: people who live in grass houses shouldn't stow thrones.

(If you don't know that one, you should be able to find it on Google without problem.)


Paul

[JHagerson]

Originally Posted by mfgoode

Fair enough!
How about using the natural logs (base e) I dont seem to get the same answer.

If our numeration system was base e (somehow) then using base e logarithms would be appropriate and it would tell us how many of the base e "e-gits" would be necessary to represent the number.

One of the things we do all of the time around here is to take a binary representation of a number (some horrendously long string of binary ones) and discuss how many decimal digits are required to represent a value of the same magnitude. In that case, the constant log_base(2)/log_base(10) (where base is e or 10, your choice) is very important.

For every additional power of 2, we need approximately 0.30103 additional decimal digit to represent it. 2^3 = 8 can be represented in one decimal digit where 2^4 = 16 requires two digits. (3*0.30103 < 1; 4*0.30103 > 1)

I hope that this helps.

[drew]

Originally Posted by R.D. Silverman

And if a person cares enough about this subject to enter into discussion
groups then they should care enough to acquire the necessary background.

So you're saying when someone does decide that they'd like to learn a little more about what they didn't pick up in high school, we should criticize their attempts to acquire the necessary background? Is a discussion group entitled 'math' not an appropriate place to acquire this background?

In any case, feel free to place high expectations for yourself, but I see no reason you you need to be so condescending of others.

And I take offense to you singling out American culture as 'dumbed down'. I have no doubt that plenty of people all over the world don't know logarithms, even though they studied them at one point in school.

Drew

[mfgoode]

[QUOTE=drew]So you're saying when someone does decide that they'd like to learn a little more about what they didn't pick up in high school, we should criticize their attempts to acquire the necessary background? Is a discussion group entitled 'math' not an appropriate place to acquire this background?

Thank you Jhagerson. Your post was most informative and you have explained the conversion formular very clearly which evidentlyI had forgotten, for a quick check. That was all I wanted clarfied-- not a criticism!

A spirited retort indeed Drew.and I agree fully with you..

In my global travels for 35years I have learnt that you cant change others. The only one you can change is yourself. You *can* correct your attitude towards them and then co-exist.
In my 1-1/2 years with mersenne forum I felt hurt and humiliated at first at unnecessary remarks and comments
Then I decided to erect in my mind a sort of mental construct of the Eratosthenes sieve. Accept all and then separate the primes (math content) from the composites (unrelated comments) as they came along in a thread.
The ego as explained by Freud is akin to a circle. The centre is the true self called the ‘I’: the circumference is what the individual thinks of himself to be. As time goes on the circle expands or contrasts depending on experience but the ‘I’ remains unchanged.
As two individuals interact the circles touch each other but no matter how small the ego is the two ‘I’s can never become one. They maintain their identities so there will always be a difference of opinion.
So what do we do?
Use the mental sieve! Reject the falsehood and retain the Truth!

[R.D. Silverman]

Originally Posted by drew

So you're saying when someone does decide that they'd like to learn a little more about what they didn't pick up in high school, we should criticize their attempts to acquire the necessary background? Is a discussion group entitled 'math' not an appropriate place to acquire this background?

In any case, feel free to place high expectations for yourself, but I see no reason you you need to be so condescending of others.

And I take offense to you singling out American culture as 'dumbed down'. I have no doubt that plenty of people all over the world don't know logarithms, even though they studied them at one point in school.

Drew

No. I am saying the exact opposite. We should criticize *NOT* picking up
the background. But many people come to this forum without doing it.
(i.e. without first picking up the required background). This forum is NOT the
place to relearn trivial and elementary mathematics. One should acquire
the background first.

The fact that many people all over the world failed to learn what they should have learned while in high school is not an excuse for people here failing to
do their homework. "Two wrongs do not make something right".

[ewmayer]

Once again, what should have remained a polite, simple, innocuous thread veers off into off-topic and flame-warrish waters. At the risk of being called an elitist snob (or heavy-handed censor, or thread nazi, or whatever), I'm locking it.

I'd like to suggest something from Dr. Silverman's own stated criteria for identifying thread cranks as a guideline as to when public derision is warranted, and that is when a poster displays WILLFUL IGNORANCE. (And even when that is the case, I suggest discretion as the better part of valor, except in the most egregious cases, e.g. those where the person is not only a blatant crank, but an aggressive-and-or-rude one at that.) Asking an honest question like the thread author did does not, in my opinion, qualify as such. So what if the poster has forgotten most of the intricacies of logarithms? They asked a simple enough question and made no grandiose claims. I expect 99.9% of people who learned this kind of stuff in school but who have not made a career involving higher (or even lower, if you consider logarithms and related algebraic concepts as such) mathematics would be unable to do the required computation without some guidance. Is it necessary to belittle those who have the honesty to admit they are among that fraction? If you've got nothing positive to contribute to a given thread, just move on. If you want to expound on the state of the world, public education, today's youth, politics or whatnot, there's already a separate Soapbox Forum for that.