Dan Antion

Sorry Mary – It’s Math

Not to blame him, but I promised Peter Nena that I’d tell my favorite story that involves logarithms.

Hang on. Don’t skip to the gallery just yet., Give me a chance to make this interesting.

Do you remember what logarithms are? If so, skip to the story. If not, you’re making it harder for me to keep this interesting. I’m going to give you a break. I am going to explain what logarithms are but I’m not going to explain why they’re good things to have and how they make our lives easier. I am only going to explain the little bit about logarithms that you need to know to appreciate my story. OK? Is it a deal? And, to make life even better, I’m going to only address logarithms in base 10, you know, the normal number system we live with.

Logarithm definition – a quantity representing the power to which 10 must be raised to produce a given number.

Example: the logarithm (log) of 100 is 2.  102 is 100. The log of 1,000 is 3. 103 is 1,000. See the pattern?

People are generally comfortable up to this point. The problem comes when you want to know the log of 529. That’s when we have to accept that we can raise 10 to a power that’s between 2 and 3. It’s 2.7234. Yep, 102.7234 is 529. I see your eyes rolling. I sense you trying to grasp multiplying 10 by itself 2.7234 times. I think I just felt half of you skip to the gallery. If you’re still here, hang one for one more thing about logarithms – then I’ll be done, I promise.

Doing simple math with logarithms is easy and powerful. To multiply two numbers, you add their logarithms. To divide one number into another, you subtract Log-a from Log-b. Take my word for it. Here’s a simple example.

12 x 44 = ? (hint, it equals 528)

The log of 12 = 1.079
The log of 44 = 1.643

If we add those, we get 2.722

Now, raise 10 to the 2.722 power (102.722) = 527.2298 Note: it would be 528 if I used more numbers to the right of the decimal point in those log values.

That’s it – that’s the end of math. Now we get onto the story which, unfortunately involves more math and a little science.

When I was in college, I was a chemistry major. I was working toward a chemistry degree, concentrating in “computer assisted analytic chemistry.” This was 1974 and my professor and I were making things up as we went along. He gave me a research project that had been sponsored by an industry group. The project had been assigned to a graduate student who did some work, but never finished. The goal was to write a computer simulation of a chemical process called Countercurrent Distribution. I won’t go into the process other than to say that it’s way of separating liquids from other liquids, it helped in the development of Penicillin and it’s kind of how your kidneys work.

In any case, it’s a long tedious process involving, at the time, an elaborate apparatus. The industry that was paying for our research typically used a machine capable of 1,000, oh, let’s call them cycles. The apparatus in our lab could manage 250 cycles, but we were trying to predict where among the 1,000 places the liquid we were looking for would settle. It was hard to extrapolate the results from 250 cycles up to 1,000. Worse, running 250 cycles took 40 hours. Hence the desire to simulate the apparatus.

The industry was using the Standard Bell curve (remember that) to approximate the results. Unfortunately, the real results were skewed off to one side of the center and the peak of the bell was higher and narrower. My job was to predict where the peak would be, and how high and wide it would be. This was easy, except for one thing – well, two things.

The Standard Bell curve.
Not accurate, but the kind of curve we were hoping to find.

At each end of the Standard Bell curve, and my simulation, the number along the X-axis approaches infinity (and negative infinity) while the number on the Y-axis approaches zero. In my simulation, the number on the Y-axis had to be divided into some other number, and computers give up when asked to divide by zero, or something so close to zero that it looks like zero.

This problem is why the graduate student never finished the project.

I spent from September to November trying to work around this problem. Finally, it occurred to me to change all the math to use logarithms. Since dividing while using logarithms involves subtraction, and computers were quite capable of subtracting zero from anything, it worked.

During my review with my professor in December, he asked if I had made any progress. I sheepishly offered, “I got the program working, but I haven’t had much time to play with the process.” I was hoping the progress I had made would be good enough for a B.

He got excited. “You got it working? How did you do that?” I explained the use of logarithms and he did the 1974 equivalent of a head slap. He reached over, shook my hand, and said, “you just earned four A’s!” Then he explained that being able to tell the industry group we had a working model would release the next wave of funding. I spent three more semesters adding features to my simulation. I received an A each semester.

This Rose of Sharon plant is always the first to bloom.
These are growing wild in our neighbor’s yard.
Enjoying the Bee Balm.
Taking advantage of a rare dry period.
Everything is green and growing. The bunnies seem to like it.
I wanted to include another power line for Peter. Maddie decided to get in the act.
Soggy flag.
Through the trees I spotted this hawk. I think he’s looking for those bunnies, too.
The storm left some damage and a puddle we don’t usually see.
On Saturday and Sunday, Maddie and I walked in the rain.
Walking in the rain provides a chance to get some interesting pictures.
“That’s close enough cowboy!”
This is an interesting mushroom.
The first double Rose of Sharon is blooming, but only on the (barely) sunny side.
We are about 2.5 mi (4 km) from the edge of the runway.
I had to include this for Peter.

80 comments

  2. Hi Dan – well now … I guess you want us to give you a star!! All I can say is congratulations … and such an interesting post … thank you. I did enjoy it … and the photos … have a good week – cheers HIlary

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    • Thanks Hilary. This research project was the basis for the advice I received to forget about chemistry and pursue a career working with computers. I’ll take that as my star. I hope you have a great week.

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  3. That was brilliant of you. Applying your mathematical skills to solve a problem is usually its own reward. There is a triumphant feeling that comes with it. A eureka! moment. Back in the day there was the Mathematical Table. We weren’t allowed to use calculators in school and we had to learn to use the Table or fail exam. One time, while discouraging us from using calculators, the teacher said that the Mathematical Table was developed without the computer, that people sat down with their bare hands and unaided memories and developed those tables. I didn’t think much about what he was saying until later on after high school. Then it occurred to me just how much brain a person would need to develop such a table, to calculate the sine or cosine of, say, 79.66 deg, or even the log of 0.567, without the aid of a computer. The commitment required is astronomical. (But then people have done even more wonderful things without the computer. The computer itself was built without the computer, something that now feels impossible.) At the university we were allowed to use calculators and the tables became history. One day in 2014 I was in a meeting and the guy next to me was multiplying 17 by 20 on his phone’s calculator. Surely! I use my calculator only for complex operations and operations involving large numbers I can’t handle inside my head. I saw a video on YouTube of a man calculating Pi up to over 200 decimals and I was tongue-tied. People are amazing out here.

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    • I once did some moderately difficult math in a meeting, to defend a decision I had made that went against company policy. Instead of being impressed, the guy criticizing my decision said, “what, did you do that in your head?” Like it was a bad thing. I was trying to show that the company policy was costing us significantly more money, and that we could determine the best choice by using math. Later, he sent me an email reminding me of the policy,

      When I managed to get this program working is when I truly understood the cumulative nature of math learning. Nothing stands alone.

      Having worked with computers from that day forward, Peter, I saw the PC being introduced. I saw the point where you needed a computer to fix a computer, and I saw the point where you needed a computer with an Internet connection to even set up a new computer. We still need to rely on our own ability. Even if we write a program to do the work, we have to know how to solve the problem.

      Thanks for your comment. I am glad you enjoyed this story. I hope you have a great week.

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      • On that one Dan, (and leaving aside logs and algebra and all that brain scrambling stuff) I’m glad to be able to do basic arithmetical calculation in my head. That is most useful in the supermarket when they try to baffle your attempts to work out the best deal for like items when one size is marked at so much per 100g or 1000g and another at so much each when there are 12 or 24 or whatever in a pack of the same product from a different supplier. Sometimes it’s the smaller pack size that’s cheaper too. Supermarkets can be really cunning at ripping people off so being able to do a quick calculation in your head can save you some serious money over time.

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  4. Seriously though. Going back to our – none too complimentary – opinions of some of our school teachers: if only they had explained it the way you just did, then I would have understood it 60-odd years ago. They always made mathematics / algebra and all that other stuff a) so freakin’ boring and b) so unnecessarily complicated whereas it can be just the opposite if the right teaching methods and attitude are applied. Now I understand what logs are I’m left wondering just what the hell I’m going to do with my new found knowledge

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    • Dig out the slide rule you once carried. It is a logarithm machine. I had teachers and professors who could only dump facts on the table, work problems on the board and hope we would understand by osmosis. I also had a few who could make us understand why we were learning what we were learning. The ones in that last group were angels in the classroom.

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  6. About the only thing I understood is that you received an “A” each semester!! I’m glad Peter is delighted with your post. I need Tylenol!! 🤗

    Even soggy, Old Glory looks grand! Great reflection shots, and MiMi seems to be feeling her oats this morning. So glad Maddie found some dry time and a dirt space on her deck to hang out. Sure hope the bunny and the hawk didn’t meet close up and personal!

    Happy Monday.
    Ginger

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    • There was a bunny that used to like to nibble along the outer edge of the ball field. I haven’t seen it for a while :(

      We’ve been walking, light rain or shine, Ginger. There no point waiting for sunshine some f these days. MiMi is feisty sometimes. I hope your week is off to a good start.

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  8. I was finished with my coffee, so I had to scan so I didn’t get a migraine, but I was glad to see you got A’s. :-) Maddie looks large and in charge of ‘her’ deck during a dry moment which was hard to find. What’s with WP? No post today from you, I can’t read the captions unless I view the smaller photos, and over the weekend when I was doing a long volunteer post I had to rekey everything because it wouldn’t let me correct. I wonder if they realize how old this is getting. Oh that’s right – they don’t care. :-) Happy Monday and stay dry.

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    • Scanning is fine, Judy. I knew better when I wrote this. To see the captions in the larger images, you have to click on the the little ‘i’ in the circle – every time – they really aren’t making it easy to be on either side of thieve pages.

      I hope you have a good week. It looks like we will see some sunshine.

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  9. Okay, well, I laughed at the title, read the definition of logarithms and moved on to the best part – the gallery. Pretty flowers and cute babies make for a good start to my Monday, Dan. Have an excellent week!

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    • Hahaha – I knew you couldn’t yell at me since it was Peter that had asked for the story. I did try tp get some nice pictures, though. I hope you have a great week, Mary. Thanks for being a good sport.

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  13. I now itch all over from the hives that blossomed as I read this. What flashbacks! I seem to see slide rules coming at me a la Twilight Zone. I understood nothing in your story except that you solved the problem, and that problem-solving is The Thing. I could only shake my head at the company guy who essentially said that company policy is more important than reason. Ah, the way of the world. Thank goodness for the cat caption, which again got me laughing and put the world back into balance.

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  15. No math or science, please. I was English and spelling all the way. My favorite part of this: the last paragraph. The teacher didn’t even have a clue! What a hoot! You absolutely deserved those 4 A’s, Dan! “That’s close enough, cowboy!” cracked me up. I needed that laugh after your dad’s mathiness, MuMu! 😹

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  16. Very belated congrats, Dan. :-) I enjoyed math a lot (it’s logical) but when I finished trig I figured I’d reached the end of its use for me, especially as it wasn’t my major or either of my double minors. Love today’s photos, too, and I hope your Monday’s off to a grand start (and your week as well.)

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  17. Yes we do need math and science even if at times it is moderately uncomfortable. It is like knowing how to use the blazes on the trail. It can get us out of the metaphorical forest and into the light. And you thought you only solved a small part of the problem. Glad your professor saw the big problem and rewarded your creativity. That is why hammers come in many sizes, all the way from a jeweler’s hammer up to a sledge. I think you deserve another A for telling the story. I am sure there are some math and science teachers that would agree. I will have to see if there is a bell curve and logarithm that can help me with my daylily crosses. Happy Monday.

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  18. Wow–What a great story! Math is like camping to me: I hate to do it, but I adore reading about other people doing it. And it’s always delightful when somebody comes up with a simple and elegant solution to a seemingly insoluble problem. Good for you!

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    • Thanks John. Up until the year before that one, I was still using a slide rule, so logarithms weren’t that far from my mind. I was upset that it took me so long to figure it out. I was thrilled to learn that the Prof was happy.

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  21. Wow. My hat is off to you and anyone who can readily understand that stuff. I could do math when I had to, but it was a slog most of the time. Hope you have a great week, Dan!

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    • Thanks Paul. I was in my prime 😏

      I like to think I could still solve that problem, but hopefully I won’t be put to the test. Still, I have some angled cabinets to make so remembering complementary angles might come in handy.

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  22. Dan, math anxiety me loved the flowers, bunny, kitty, Maddie, and the reflections in the water photos. Also kudos to you for solving the problem and getting all As. Can’t believe I read the whole post. What was I thinking? Nothing mathematical registered. But, you did a great job explaining. Have an awesome week. Rest your brain. 📚 Christine

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  24. Oh gosh, I can’t believe I was once a bio major. Thankfully, I realized it wasn’t my field by taking chemistry (and physics). Your post brought back memories long buried. If you had taught the courses, well, maybe I could have understood a bit better. Fun post, Dan. 🙂

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    • Chemistry and physics have a way of convincing people to change majors ;-) I hope you enjoyed those memories. It’s funny to think back on an era before personal computers and smart phones.

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  26. Real, Dan? Math homework on your blog! Oh vey, you start talking about middle school math and I begin to get anxious. There’s not going to be a pop quiz later this week, is there?

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  27. I have NEVER had a break-through moment like that in math, and doubt I ever will. How exciting for you though!! I got goosebumps for you reading what your professor said to you. Four A’s!! In Math! That’s never going to be me. 😂

    The puddle reflections and flowers are lovely!

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    • Very good guess. Punch cards, one full box and a little more for the main program, and the rest of the second box for functions and data. FORTRAN IV. I worked out of a remote data center. We had a PDP 11 that buffered the program and submitted it to an IBM 360. If I bribed the operator with coffee, she would run a “compile for syntax” – otherwise, it was submit and come back tomorrow. The program used almost a full minute of CPU time, and was given a miserably low priority. Any time I made significant changes, I’d go get her a cup of coffee, sometimes, a donut. Then, if I fixed a syntax error, she’d run it again.

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  29. I started college as a biology major. It was the ? collateral requirements ? of higher math and chemistry that led me to change to psychology. (I hadn’t even gotten to physics.) But I used to be able to do logarithms once upon a time. Thanks for the delightful gallery!

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  31. Noooo!!! I read the definition twice, shook my head, and forged on. Aren’t you proud of me? Ha!
    Still waiting for it to ‘click’. Thanks for trying, Dan. The Rose of Sharon is gorgeous! BTW, Hubby and grandson went through the old HO scale trains. Thought of you. Really nice!

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